qu.1.topic=Charge in E-Field@

qu.1.1.mode=Inline@
qu.1.1.name=Velocity Selector - Find B - 2 ~ NG@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=<p>In a velocity selector, the forces due to a magnetic field and an electric field cancel eachother, for one velocity of charged particle:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>qE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qvB</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rArr;</mo><mi>v</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>E</mi><mrow><mi>B</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;We are given the electric field and the velocity, so we can find the magnitude of the magnetic field.</p>
<p>Assume that the charge is positive and determine which direction the electric force will be - the magnetic force must be in the opposite direction.&nbsp; Still assuming the charge is positive, use <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>F</mi></mrow><mi>&rarr;</mi></mover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>q</mi><mrow><mover><mrow><mi>v</mi></mrow><mi>&rarr;</mi></mover></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&times;</mo></mrow><mrow><mover><mrow><mi>B</mi></mrow><mi>&rarr;</mi></mover></mrow></mrow></mstyle></math>&nbsp;to determine the direction of the magnetic field.</p>
<p>&nbsp;</p>@
qu.1.1.algorithm=$E=rand(1.00,9.99,3);
$Eex=range(5,13);
$v=rand(1.00,9.99,3);
$vex=range(2,7);
$ans=($E*10^($Eex))/($v*10^($vex));@
qu.1.1.uid=c6a1824e-8f6f-4faf-9577-679824f24334@
qu.1.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Motion of Charged Particles in Electromagnetic Fields;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.1.1.part.2.answer.2=- x@
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qu.1.1.question=<p>A velocity selector is set up as in the diagram with uniform electric and magnetic fields. If the electric <br />field is of magnitude&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$E</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Eex</mi></mrow></msup><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math> and&nbsp;a charged particle of speed <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup><mfrac><mrow><mi>m</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>&nbsp;will pass<br />through undeflected, what is the magnitude in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>T</mi></mrow></mstyle></math>&nbsp;and direction of the magnetic field?</p><p><img alt="" align="middle" width="600" height="171" src="__BASE_URI__img/MagneticFields/VelocitySelector/DiagramNoB2.png" /></p><p>&nbsp;</p><p><span>Magnitude:&nbsp;&nbsp;&nbsp;<span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>T</mi></mrow></mstyle></math></span></span></p><p><span>Direction:&nbsp;&nbsp;<span>&nbsp;</span><2><span>&nbsp;</span></span></p>@

qu.1.2.mode=Inline@
qu.1.2.name=Velocity Selector - Find E - 1 ~ NG@
qu.1.2.comment=@
qu.1.2.editing=useHTML@
qu.1.2.solution=<p>In a velocity selector, the forces due to a magnetic field and an electric field cancel eachother, for one velocity of charged particle:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>qE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qvB</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rArr;</mo><mi>v</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>E</mi><mrow><mi>B</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given the magnetic field and the velocity to calculate the magnitude of the electric field.</p>
<p>Assuming the charge is positive, use <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>F</mi></mrow><mi>&rarr;</mi></mover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>q</mi><mrow><mover><mrow><mi>v</mi></mrow><mi>&rarr;</mi></mover></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&times;</mo></mrow><mrow><mover><mrow><mi>B</mi></mrow><mi>&rarr;</mi></mover></mrow></mrow></mstyle></math>&nbsp;to determine the direction of the magnetic force - the electric <em>force</em> must be in the opposite direction.&nbsp; Again, assume that the charge is positive and determine the direction of the electric <em>field.</em></p>
<p>&nbsp;</p>@
qu.1.2.algorithm=$B=rand(1.00,9.99,3);
$Bex=range(2,10);
$v=rand(1.00,9.99,3);
$vex=range(2,7);
$ans=($B*10^($Bex))*($v*10^($vex));@
qu.1.2.uid=5d2d7fd6-9dc3-42f9-9f3b-ba6de71a26d5@
qu.1.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Motion of Charged Particles in Electromagnetic Fields;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.1.2.question=<p>A velocity selector is set up as in the diagram with uniform electric and magnetic fields. If the magnetic<br />field is of magnitude&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$B</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Bex</mi></mrow></msup><mi>T</mi></mrow></mstyle></math> and&nbsp;a charged particle of speed <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup><mfrac><mrow><mi>m</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>&nbsp;will pass<br />through undeflected, what is the magnitude in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>&nbsp;and direction of the magnetic field?</p><p><img alt="" align="middle" width="600" height="171" src="__BASE_URI__img/MagneticFields/VelocitySelector/DiagramNoE1.png" /></p><p>&nbsp;</p><p><span>Magnitude:&nbsp;&nbsp;&nbsp;<span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math></span></span></p><p><span>Direction:&nbsp;&nbsp;<span>&nbsp;</span><2><span>&nbsp;</span></span></p>@

qu.1.3.mode=Inline@
qu.1.3.name=Charge Gun - Find Displacement - Algebraic ~ NGc@
qu.1.3.comment=@
qu.1.3.editing=useHTML@
qu.1.3.solution=<p>Between the plates, the charge will have an electric force acting on it equal to <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>qE</mi></mrow></mstyle></math>.&nbsp; The acceleration due to this force will be <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>qE</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>.&nbsp; It will take the particle a time <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>t</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msub><mi>x</mi><mrow><mn>1</mn></mrow></msub><mrow><mi>v</mi></mrow></mfrac></mrow></mstyle></math> to pass through the plates.&nbsp; As a result, the particle will have travelled a vertical distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>&Delta;y</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac><mfrac><mi>qE</mi><mrow><mi>m</mi></mrow></mfrac><mfrac><msubsup><mi>x</mi><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mrow><msup><mi>v</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mstyle></math>&nbsp;and have a vertical speed of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>v</mi><mrow><mi>y</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mrow><msub><mi>qEx</mi><mrow><mn>1</mn></mrow></msub></mrow><mrow><mi>mv</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>After exiting the plate region, the particle will no longer be under acceleration.&nbsp; Since the horizontal speed has not changed, the time to reach the screen after exiting the plates will be<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>t</mi><mrow><mn>2</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msub><mi>x</mi><mrow><mn>2</mn></mrow></msub><mrow><mi>v</mi></mrow></mfrac></mrow></mstyle></math>.&nbsp; During this time, it will travel&nbsp;a vertical distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>&Delta;y</mi><mrow><mn>2</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msub><mi>x</mi><mrow><mn>2</mn></mrow></msub><msub><mi>qEx</mi><mrow><mn>1</mn></mrow></msub></mrow><mrow><msup><mi>mv</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Therefore, the particle will hit the screen at a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Delta;y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msub><mi>qEx</mi><mrow><mn>1</mn></mrow></msub><mrow><msup><mi>mv</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mfenced open='(' close=')' separators=','><mrow><mfrac><msub><mi>x</mi><mrow><mn>1</mn></mrow></msub><mrow><mn>2</mn></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>x</mi><mrow><mn>2</mn></mrow></msub></mrow></mfenced></mrow></mstyle></math>&nbsp;from <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>.</p>@
qu.1.3.algorithm=$mc=maple("(q*E*x1/(m*v^2))*((x1/2)+x2)");@
qu.1.3.uid=43d6c0ac-7436-49a2-bade-579d6e8538df@
qu.1.3.info=  Course=Introductory Electricity and Magnetism;
  Topic=Motion of Charges in Electric Fields;
  Author=Aron Pasieka;
  Difficulty=Hard;
  Features=Diagram;
@
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qu.1.3.part.1.answer=$mc@
qu.1.3.part.1.mode=Formula@
qu.1.3.question=<p align="left">A particle with charge q>0 and mass m is fired from a gun, with an initial speed v in the <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mi>i</mi><mi>&#x005e;</mi></mover></mrow></mstyle></math>&nbsp;direction.&nbsp;&nbsp; The particle&nbsp;passes<br />through a region between two plates where the electric field is (approximately)&nbsp;uniform&nbsp;and equal to E. The particle<br />then passes through a region with no fields, before finally hitting a&nbsp;screen.</p><p>&nbsp;</p><p>&nbsp;</p><div align="center"><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="600" height="266"><param name="image" value="__BASE_URI__img/ElectricFields/ChargeGun-FindElectricField/Diagram.png" /><param name="size" value="3" /><param name="label.1.x" value="322" /><param name="label.1.y" value="30" /><param name="label.1.text" value="x1" /><param name="label.2.x" value="487" /><param name="label.2.y" value="30" /><param name="label.2.text" value="x2" /><param name="label.3.x" value="200" /><param name="label.3.y" value="130" /><param name="label.3.text" value="q" /></applet></p><p align="left">&nbsp;</p><p align="left">Relative to the point P, where does the particle hit the screen?&nbsp; Provide an algebraic answer in terms of&nbsp;<br />the&nbsp;given parameters.&nbsp; Neglect gravity.&nbsp;</p></div><p><1></p>@

qu.1.4.mode=Inline@
qu.1.4.name=Velocity Selector - Find B - 1 ~ NG@
qu.1.4.comment=@
qu.1.4.editing=useHTML@
qu.1.4.solution=<p>In a velocity selector, the forces due to a magnetic field and an electric field cancel eachother, for one velocity of charged particle:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>qE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qvB</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rArr;</mo><mi>v</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>E</mi><mrow><mi>B</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;We are given the electric field and the velocity, so we can find the magnitude of the magnetic field.</p>
<p>Assume that the charge is positive and determine which direction the electric force will be - the magnetic force must be in the opposite direction.&nbsp; Still assuming the charge is positive, use <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>F</mi></mrow><mi>&rarr;</mi></mover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>q</mi><mrow><mover><mrow><mi>v</mi></mrow><mi>&rarr;</mi></mover></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&times;</mo></mrow><mrow><mover><mrow><mi>B</mi></mrow><mi>&rarr;</mi></mover></mrow></mrow></mstyle></math>&nbsp;to determine the direction of the magnetic field.</p>
<p>&nbsp;</p>@
qu.1.4.algorithm=$E=rand(1.00,9.99,3);
$Eex=range(5,13);
$v=rand(1.00,9.99,3);
$vex=range(2,7);
$ans=($E*10^($Eex))/($v*10^($vex));@
qu.1.4.uid=23ae0511-7cfb-4add-9ccb-509733a85a30@
qu.1.4.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Motion of Charged Particles in Electromagnetic Fields;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.1.4.part.2.answer.5=+ z@
qu.1.4.part.2.answer.4=- y@
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qu.1.4.part.2.answer.2=- x@
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qu.1.4.question=<p>A velocity selector is set up as in the diagram with uniform electric and magnetic fields. If the electric <br />field is of magnitude&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$E</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Eex</mi></mrow></msup><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math> and&nbsp;a charged particle of speed <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup><mfrac><mrow><mi>m</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>&nbsp;will pass<br />through undeflected, what is the magnitude in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>T</mi></mrow></mstyle></math>&nbsp;and direction of the magnetic field?</p><p><img alt="" align="middle" width="600" height="171" src="__BASE_URI__img/MagneticFields/VelocitySelector/DiagramNoB1.png" /></p><p>&nbsp;</p><p><span>Magnitude:&nbsp;&nbsp;&nbsp;<span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>T</mi></mrow></mstyle></math></span></span></p><p><span>Direction:&nbsp;&nbsp;<span>&nbsp;</span><2><span>&nbsp;</span></span></p>@

qu.1.5.mode=Inline@
qu.1.5.name=Charge vs Gravity - Find Charge ~ NG@
qu.1.5.comment=@
qu.1.5.editing=useHTML@
qu.1.5.solution=<p>If a charged particle is held motionless by gravity and an electric field, then:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>mg</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qE</mi></mrow></mstyle></math>.</p>
<p>&nbsp;We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>E</mi></mrow></mstyle></math>.&nbsp; The force of gravity will be downwards, so the direction of the electric field must combine with the sign of the charge to result in an electric&nbsp;force upwards.</p>@
qu.1.5.algorithm=$m=rand(1.0,9.8,3);
$mex=range(20,40);
$E=rand(1.0,9.8,3);
$Eex=range(15,25);
$idx=range(0,1);
$EDir=switch($idx,'upwards','downwards');
$corDir=switch($idx,'Positive','Negative');
$incDir=switch($idx,'Negative','Positive');
$ans=($m*10^(-$mex))*9.80/($E*10^(-$Eex));@
qu.1.5.uid=fd409d63-8c4e-45d1-9f65-56ce514bffab@
qu.1.5.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Forces on Charged Particles in an Electric Field;
  Difficulty=Medium;
  Features=Algorithmic;
@
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qu.1.5.part.2.question=(Unset)@
qu.1.5.part.2.answer.2=$incDir@
qu.1.5.part.2.answer.1=$corDir@
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qu.1.5.question=<p>A charged particle of mass&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$mex</mi></mrow></msup><mi>kg</mi></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>&nbsp;is suspended motionless in the air by an electric field.<br />If the electric field is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$E</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Eex</mi></mrow></msup><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>&nbsp;$EDir, what is the magnitude (in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>)&nbsp;and sign of the charge of&nbsp;<br />the particle?</p><p><br />Magnitude:&nbsp;<span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math><br /><br />Sign:&nbsp; </span><2><span>&nbsp;</span></p>@

qu.1.6.mode=Inline@
qu.1.6.name=Velocity Selector - Find E - 2 ~ NG@
qu.1.6.comment=@
qu.1.6.editing=useHTML@
qu.1.6.solution=<p>In a velocity selector, the forces due to a magnetic field and an electric field cancel eachother, for one velocity of charged particle:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>qE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qvB</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rArr;</mo><mi>v</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>E</mi><mrow><mi>B</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given the velocity and the magnetic field, which we can use to calculate the magnitude of the electric field.</p>
<p>Assuming the charge is positive, use <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>F</mi></mrow><mi>&rarr;</mi></mover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>q</mi><mrow><mover><mrow><mi>v</mi></mrow><mi>&rarr;</mi></mover></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&times;</mo></mrow><mrow><mover><mrow><mi>B</mi></mrow><mi>&rarr;</mi></mover></mrow></mrow></mstyle></math>&nbsp;to determine the direction of the magnetic force - the electric <em>force</em> must be in the opposite direction.&nbsp; Again, assume that the charge is positive and determine the direction of the electric <em>field.</em></p>
<p>&nbsp;</p>@
qu.1.6.algorithm=$B=rand(1.00,9.99,3);
$Bex=range(2,10);
$v=rand(1.00,9.99,3);
$vex=range(2,7);
$ans=($B*10^($Bex))*($v*10^($vex));@
qu.1.6.uid=54f592eb-61a1-49a4-b0f2-fc88287f9e29@
qu.1.6.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Motion of Charged Particles in Electromagnetic Fields;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.1.6.part.2.name=sro_id_2@
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qu.1.6.question=<p>A velocity selector is set up as in the diagram with uniform electric and magnetic fields. If the magnetic<br />field is of magnitude&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$B</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Bex</mi></mrow></msup><mi>T</mi></mrow></mstyle></math> and&nbsp;a charged particle of speed <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup><mfrac><mrow><mi>m</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>&nbsp;will pass<br />through undeflected, what is the magnitude in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>&nbsp;and direction of the magnetic field?</p><p><img alt="" align="middle" width="600" height="171" src="__BASE_URI__img/MagneticFields/VelocitySelector/DiagramNoE2.png" /></p><p>&nbsp;</p><p><span>Magnitude:&nbsp;&nbsp;&nbsp;<span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math></span></span></p><p><span>Direction:&nbsp;&nbsp;<span>&nbsp;</span><2><span>&nbsp;</span></span></p>@

qu.1.7.mode=Inline@
qu.1.7.name=Velocity Selector - Find v - 2 ~ NG@
qu.1.7.comment=@
qu.1.7.editing=useHTML@
qu.1.7.solution=<p>In a velocity selector, the forces due to a magnetic field and an electric field cancel eachother, for one velocity of charged particle:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>qE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qvB</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rArr;</mo><mi>v</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>E</mi><mrow><mi>B</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are&nbsp;given the electric and magnetic fields.&nbsp;</p>@
qu.1.7.algorithm=$E=rand(1.00,9.99,3);
$Eex=range(5,13);
$v=range(10000,299790000);
$B=rand(1.00,9.99,3);
$Bex=int(log($v))-1;
$ans=($E*10^($Eex))/($B*10^($Bex));@
qu.1.7.uid=8f358507-83a8-4776-a241-e3b7eca91104@
qu.1.7.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Motion of Charged Particles in Electromagnetic Fields;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
qu.1.7.weighting=1@
qu.1.7.numbering=alpha@
qu.1.7.part.1.name=sro_id_1@
qu.1.7.part.1.answer.units=@
qu.1.7.part.1.numStyle= scientific  @
qu.1.7.part.1.editing=useHTML@
qu.1.7.part.1.showUnits=false@
qu.1.7.part.1.question=(Unset)@
qu.1.7.part.1.mode=Numeric@
qu.1.7.part.1.grading=exact_sigd@
qu.1.7.part.1.negStyle=both@
qu.1.7.part.1.digit=3@
qu.1.7.part.1.answer.num=$ans@
qu.1.7.question=<p>A velocity selector is set up as in the diagram with uniform electric and magnetic fields. If the electric <br />field is of magnitude&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$E</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Eex</mi></mrow></msup><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math> and the magnetic field is of magnitude <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$B</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Bex</mi></mrow></msup><mi>T</mi></mrow></mstyle></math>, what <br />speed of charged particle will pass through undeflected, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>?</p><p><img alt="" align="middle" width="600" height="171" src="__BASE_URI__img/MagneticFields/VelocitySelector/Diagram2.png" /></p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math></span></p>@

qu.1.8.mode=Inline@
qu.1.8.name=Velocity Selector - Find v - 1 ~ NG@
qu.1.8.comment=@
qu.1.8.editing=useHTML@
qu.1.8.solution=<p>In a velocity selector, the forces due to a magnetic field and an electric field cancel eachother, for one velocity of charged particle:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>qE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qvB</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rArr;</mo><mi>v</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>E</mi><mrow><mi>B</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given the electric and magnetic fields.</p>@
qu.1.8.algorithm=$E=rand(1.00,9.99,3);
$Eex=range(5,13);
$v=range(10000,299790000);
$B=rand(1.00,9.99,3);
$Bex=int(log($v))-1;
$ans=($E*10^($Eex))/($B*10^($Bex));@
qu.1.8.uid=c1154cf6-0968-4ff9-93d8-bf3902bfb182@
qu.1.8.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Motion of Charged Particles in Electromagnetic Fields;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
qu.1.8.weighting=1@
qu.1.8.numbering=alpha@
qu.1.8.part.1.name=sro_id_1@
qu.1.8.part.1.answer.units=@
qu.1.8.part.1.numStyle= scientific  @
qu.1.8.part.1.editing=useHTML@
qu.1.8.part.1.showUnits=false@
qu.1.8.part.1.question=(Unset)@
qu.1.8.part.1.mode=Numeric@
qu.1.8.part.1.grading=exact_sigd@
qu.1.8.part.1.negStyle=both@
qu.1.8.part.1.digit=3@
qu.1.8.part.1.answer.num=$ans@
qu.1.8.question=<p>A velocity selector is set up as in the diagram with uniform electric and magnetic fields. If the electric <br />field is of magnitude&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$E</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Eex</mi></mrow></msup><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math> and the magnetic field is of magnitude <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$B</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Bex</mi></mrow></msup><mi>T</mi></mrow></mstyle></math>, what <br />speed of charged particle will pass through undeflected, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>?</p><p><img alt="" align="middle" width="600" height="171" src="__BASE_URI__img/MagneticFields/VelocitySelector/Diagram1.png" /></p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math></span></p>@

qu.1.9.mode=Inline@
qu.1.9.name=Charged Balloon vs Gravity - Find Free Electrons ~ NG@
qu.1.9.comment=@
qu.1.9.editing=useHTML@
qu.1.9.solution=<p>If&nbsp;the charged balloon is held motionless by gravity and an electric field, then:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>mg</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qE</mi></mrow></mstyle></math>.</p>
<p>&nbsp;We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>E</mi></mrow></mstyle></math>&nbsp;which allows us to calculate <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>q</mi></mrow></mstyle></math>.&nbsp; We can then find the number of free electrons by using <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>q</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>n</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>e</mi></mrow></mstyle></math>.</p>@
qu.1.9.algorithm=$m=rand(0.2,9.9,3);
$E=rand(0.5,9.9,3);
$eex=range(10,12);
$n=($m/1000)/(1.60*10^(-19)*$E*10^($eex));@
qu.1.9.uid=230ac2cc-b3eb-4e31-8ac1-c95ec0ff94aa@
qu.1.9.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Charges in an Electric Field;
  Difficulty=Hard;
  Features=Algorithmic;
@
qu.1.9.weighting=1@
qu.1.9.numbering=alpha@
qu.1.9.part.1.name=sro_id_1@
qu.1.9.part.1.answer.units=@
qu.1.9.part.1.numStyle= scientific  @
qu.1.9.part.1.editing=useHTML@
qu.1.9.part.1.showUnits=false@
qu.1.9.part.1.question=(Unset)@
qu.1.9.part.1.mode=Numeric@
qu.1.9.part.1.grading=exact_sigd@
qu.1.9.part.1.negStyle=both@
qu.1.9.part.1.digit=3@
qu.1.9.part.1.answer.num=$n@
qu.1.9.question=<p>After rubbing a balloon against someone's hair, a balloon has accumulated a static electric charge.&nbsp; The<br />air inside the balloon has the same density as the air outside of the balloon, and the balloon itself&nbsp;<br />weighs&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mN</mi></mrow></mstyle></math>.&nbsp;&nbsp;How many free electrons are there on the surface of the balloon if an electric field of<br />magnitude&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$E</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$eex</mi></mrow></msup><mfrac><mi>N</mi><mrow><mi>m</mi></mrow></mfrac></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>&nbsp;is required to keep the balloon floating at a constant height?</p><p><br /><1><span>&nbsp;<br /></span></p>@

qu.1.10.mode=Inline@
qu.1.10.name=Charged Balloon vs Gravity - Find Mass ~ NG@
qu.1.10.comment=@
qu.1.10.editing=useHTML@
qu.1.10.solution=<p>If&nbsp;the charged balloon is held motionless by gravity and an electric field, then:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>mg</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qE</mi></mrow></mstyle></math>.</p>
<p>&nbsp;We are given&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>q</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>n</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>e</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>E</mi></mrow></mstyle></math>.</p>@
qu.1.10.algorithm=$E=rand(0.5,9,3);
$eex=range(10,12);
$n=range(600000,900000);
$m=$n*1000*(1.60*10^(-19)*$E*10^($eex))/(9.80);@
qu.1.10.uid=682cc34c-fc75-4b20-ac21-8dba70ec173d@
qu.1.10.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Charges in an Electric Field;
  Difficulty=Hard;
  Features=Algorithmic;
@
qu.1.10.weighting=1@
qu.1.10.numbering=alpha@
qu.1.10.part.1.name=sro_id_1@
qu.1.10.part.1.answer.units=@
qu.1.10.part.1.numStyle= scientific  @
qu.1.10.part.1.editing=useHTML@
qu.1.10.part.1.showUnits=false@
qu.1.10.part.1.question=(Unset)@
qu.1.10.part.1.mode=Numeric@
qu.1.10.part.1.grading=exact_sigd@
qu.1.10.part.1.negStyle=both@
qu.1.10.part.1.digit=3@
qu.1.10.part.1.answer.num=$m@
qu.1.10.question=<p>After rubbing a balloon against someone's hair, a balloon has accumulated a static electric charge.&nbsp; The<br />air inside the balloon has the same density as the air outside of the balloon.&nbsp;&nbsp;If there are&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$n</mi></mrow></mstyle></math> free electrons<br />on the surface of the balloon and&nbsp;an electric field of magnitude&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$E</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$eex</mi></mrow></msup><mfrac><mi>N</mi><mrow><mi>m</mi></mrow></mfrac></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>&nbsp;is required to keep the&nbsp;<br />balloon floating at a constant height, what is the mass of the balloon, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>g</mi></mrow></mstyle></math>?</p><p><br /><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>g</mi></mrow></mstyle></math><br /></span></p>@

qu.1.11.mode=Inline@
qu.1.11.name=Charge vs Gravity - Find Electric Field ~ NG@
qu.1.11.comment=@
qu.1.11.editing=useHTML@
qu.1.11.solution=<p>If a charged particle is held motionless by gravity and an electric field, then:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>mg</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>qE</mi></mrow></mstyle></math>.</p>
<p>&nbsp;We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>q</mi></mrow></mstyle></math>.&nbsp; The force of gravity will be downwards, so the direction of the electric field must combine with the sign of the charge to result in an electric&nbsp;force upwards.</p>@
qu.1.11.algorithm=$m=rand(1.0,9.8,3);
$mex=range(20,40);
$qex=range(2,15);
$idx=range(0,1);
$q=switch($idx,-rand(1.0,9.8,3),+rand(1.0,9.8,3));
$corDir=switch($idx,'Down','Up');
$incDir=switch($idx,'Up','Down');
$ans=($m*10^(-$mex))*9.80/($q*10^(-$qex));@
qu.1.11.uid=d1fc489a-fb15-4523-860e-a05aa2fde4bd@
qu.1.11.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Difficulty=Medium;
  Topic=Forces on Charged Particles in an Electric Field;
  Features=Algorithmic;
@
qu.1.11.weighting=1,1@
qu.1.11.numbering=alpha@
qu.1.11.part.1.name=sro_id_1@
qu.1.11.part.1.answer.units=@
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qu.1.11.part.1.editing=useHTML@
qu.1.11.part.1.showUnits=false@
qu.1.11.part.1.question=(Unset)@
qu.1.11.part.1.mode=Numeric@
qu.1.11.part.1.grading=exact_sigd@
qu.1.11.part.1.negStyle=both@
qu.1.11.part.1.digit=3@
qu.1.11.part.1.answer.num=$ans@
qu.1.11.part.2.grader=exact@
qu.1.11.part.2.name=sro_id_2@
qu.1.11.part.2.editing=useHTML@
qu.1.11.part.2.answer.5=Not enough information@
qu.1.11.part.2.display.permute=true@
qu.1.11.part.2.answer.4=Right@
qu.1.11.part.2.answer.3=Left@
qu.1.11.part.2.question=(Unset)@
qu.1.11.part.2.answer.2=$incDir@
qu.1.11.part.2.answer.1=$corDir@
qu.1.11.part.2.mode=List@
qu.1.11.part.2.display=menu@
qu.1.11.part.2.credit.5=0.0@
qu.1.11.part.2.credit.4=0.0@
qu.1.11.part.2.credit.3=0.0@
qu.1.11.part.2.credit.2=0.0@
qu.1.11.part.2.credit.1=1.0@
qu.1.11.question=<p>A charged particle of mass&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$mex</mi></mrow></msup><mi>kg</mi></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>&nbsp;is suspended motionless in the air by an electric field.<br />If the charge on the particle is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$q</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$qex</mi></mrow></msup><mi>C</mi></mrow></mstyle></math>, what is the magnitude (in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>) and direction of the&nbsp;<br />electric field?</p><p><br />Magnitude:&nbsp;<span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math><br /><br />Direction:&nbsp; </span><2><span>&nbsp;</span></p>@

qu.2.topic=Capacitance@

qu.2.1.mode=Inline@
qu.2.1.name=Capacitance - Coaxial - Find L ~ NGc@
qu.2.1.comment=@
qu.2.1.editing=useHTML@
qu.2.1.solution=<p>The capacitance per unit length for a cylindrical capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mi>C</mi><mrow><mi>L</mi></mrow></mfrac></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mn>2</mn><mrow><mi>&pi;</mi></mrow><mrow><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub></mrow></mrow><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><msub><mi>r</mi><mrow><mi>out</mi></mrow></msub><mrow><msub><mi>r</mi><mrow><mi>inner</mi></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Therefore:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>L</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>C</mi><mrow><mn>2</mn><mrow><mi>&pi;</mi></mrow><mrow><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><msub><mi>r</mi><mrow><mi>out</mi></mrow></msub></mrow><mrow><msub><mi>r</mi><mrow><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>in</mo></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mrow><mrow><mi></mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>L</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$C</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Cex</mi></mrow></msup><mi>F</mi></mrow></mfenced></mrow><mrow><mn>2</mn><mrow><mi>&pi;</mi></mrow><mrow><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$rout</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi>$rin</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow><mrow><mi mathvariant='normal'></mi></mrow></mstyle></math></p>@
qu.2.1.algorithm=$rin=rand(0.2,15,3);
$rout=rand($rin,25,3);
$C=rand(1.00,9.99,3);
$Cex=range(4,7);
$mc=maple("evalf(($C*10^(-$Cex))/(2*Pi*8.854187817*10^(-12)/ln($rout/$rin)));
");@
qu.2.1.uid=8f3b18b0-7a1b-47e5-9364-63f42c3a245b@
qu.2.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitance;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.2.1.weighting=1@
qu.2.1.numbering=alpha@
qu.2.1.part.1.name=sro_id_1@
qu.2.1.part.1.answer.units=@
qu.2.1.part.1.numStyle= scientific  @
qu.2.1.part.1.editing=useHTML@
qu.2.1.part.1.showUnits=false@
qu.2.1.part.1.question=(Unset)@
qu.2.1.part.1.mode=Numeric@
qu.2.1.part.1.grading=exact_sigd@
qu.2.1.part.1.negStyle=both@
qu.2.1.part.1.digit=3@
qu.2.1.part.1.answer.num=$mc@
qu.2.1.question=<p>A cylindrical capacitor has inner and outer radii as labelled in following diagram.</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="400" height="420"><param name="image" value="__BASE_URI__img/Capacitance/Capacitance-Coaxial/Diagram.png" /><param name="size" value="4" /><param name="label.1.x" value="83" /><param name="label.1.y" value="24" /><param name="label.1.text" value="$rout mm" /><param name="label.2.x" value="315" /><param name="label.2.y" value="42" /><param name="label.2.text" value="$rin mm" /><param name="label.3.x" value="85" /><param name="label.3.y" value="150" /><param name="label.3.text" value="+D" /><param name="label.4.x" value="310" /><param name="label.4.y" value="150" /><param name="label.4.text" value="-D" /></applet></p><p>Assume that the surface charge densities are&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>D</mi></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>D</mi></mrow></mstyle></math>.&nbsp; Find the length of capacitor required&nbsp;<br />to acheive&nbsp;a capacitance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$C</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Cex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>.</p><p><span>&nbsp;</span><1><span>&nbsp;</span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math></p>@

qu.2.2.mode=Inline@
qu.2.2.name=Capacitance - Coaxial - Find C/L ~ NGc@
qu.2.2.comment=@
qu.2.2.editing=useHTML@
qu.2.2.solution=<p>The capacitance per unit length for a cylindrical capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mi>C</mi><mrow><mi>L</mi></mrow></mfrac></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mn>2</mn><mrow><mi>&pi;</mi></mrow><mrow><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub></mrow></mrow><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><msub><mi>r</mi><mrow><mi>out</mi></mrow></msub><mrow><msub><mi>r</mi><mrow><mi>inner</mi></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Therefore:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mi>C</mi><mrow><mi>L</mi></mrow></mfrac></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mn>2</mn><mrow><mi>&pi;</mi></mrow><mrow><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub></mrow></mrow><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$rout</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi>$rin</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mfrac></mrow></mstyle></math></p>@
qu.2.2.algorithm=$rin=rand(0.2,15,3);
$rout=rand($rin,25,3);
$mc=maple("evalf(2*Pi*8.854187817*10^(-12)/ln($rout/$rin));
");@
qu.2.2.uid=dadbb1a4-6e99-4b94-bfa7-9d4517bf95e0@
qu.2.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitance;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.2.2.weighting=1@
qu.2.2.numbering=alpha@
qu.2.2.part.1.name=sro_id_1@
qu.2.2.part.1.answer.units=@
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qu.2.2.part.1.editing=useHTML@
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qu.2.2.part.1.negStyle=both@
qu.2.2.part.1.digit=3@
qu.2.2.part.1.answer.num=$mc@
qu.2.2.question=<p>A cylindrical capacitor has inner and outer radii as labelled in following diagram.</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="400" height="420"><param name="image" value="__BASE_URI__img/Capacitance/Capacitance-Coaxial/Diagram.png" /><param name="size" value="4" /><param name="label.1.x" value="83" /><param name="label.1.y" value="24" /><param name="label.1.text" value="$rout mm" /><param name="label.2.x" value="315" /><param name="label.2.y" value="42" /><param name="label.2.text" value="$rin mm" /><param name="label.3.x" value="85" /><param name="label.3.y" value="150" /><param name="label.3.text" value="+D" /><param name="label.4.x" value="310" /><param name="label.4.y" value="150" /><param name="label.4.text" value="-D" /></applet></p><p>Assuming that the surface charge densities are&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>D</mi></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>D</mi></mrow></mstyle></math>, calculate<br />the capacitance per unit length&nbsp;of the capacitor, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>F</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>.</p><p><span>&nbsp;</span><1><span>&nbsp;</span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>F</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math></p>@

qu.2.3.mode=Inline@
qu.2.3.name=Energy Stored in Capacitor - Find Electrons ~ NG@
qu.2.3.comment=@
qu.2.3.editing=useHTML@
qu.2.3.solution=<p>The energy stored in a capacitor can be expressed as:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>U</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msup><mi>Q</mi><mrow><mn>2</mn></mrow></msup><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>C</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>U</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$U</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>J</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$C</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Cex</mi></mrow></msup><mi>F</mi></mrow></mfenced></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>.</p>
<p>The total charge can then be divided by <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>e</mi></mrow></mstyle></math>&nbsp;to find the number of electrons.</p>@
qu.2.3.algorithm=$U=rand(0.1,0.999,3);
$C=rand(1.00,9.99,3);
$Cex=range(5,9);
$ans=sqrt(2*($C*10^(-$Cex))*$U)/(1.60*10^(-19));
$wPlate=switch(rint(2),'positive','negative');@
qu.2.3.uid=c8b535f9-dcee-4b9d-a3ad-161c7bdda1c1@
qu.2.3.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Energy Stored in a Capacitor;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.2.3.weighting=1@
qu.2.3.numbering=alpha@
qu.2.3.part.1.name=sro_id_1@
qu.2.3.part.1.answer.units=@
qu.2.3.part.1.numStyle= scientific  @
qu.2.3.part.1.editing=useHTML@
qu.2.3.part.1.showUnits=false@
qu.2.3.part.1.question=(Unset)@
qu.2.3.part.1.mode=Numeric@
qu.2.3.part.1.grading=exact_sigd@
qu.2.3.part.1.negStyle=both@
qu.2.3.part.1.digit=3@
qu.2.3.part.1.answer.num=$ans@
qu.2.3.question=<p>A spherical capacitor has&nbsp;a capacitance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$C</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Cex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>.&nbsp; When&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$U</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>J</mi></mrow></mstyle></math>&nbsp;of energy are stored in the&nbsp;<br />capacitor, how many&nbsp;electrons are on the&nbsp;$wPlate plate?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.2.4.mode=Inline@
qu.2.4.name=Energy Stored in Capacitor - Find Capacitance ~ NG@
qu.2.4.comment=@
qu.2.4.editing=useHTML@
qu.2.4.solution=<p>The energy stored in a capacitor can be expressed as:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>U</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msup><mi>Q</mi><mrow><mn>2</mn></mrow></msup><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>C</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>U</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$U</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>J</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Q</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mfenced><mi>e</mi></mrow></mstyle></math>.</p>@
qu.2.4.algorithm=$U=rand(1.00,9.99,3);
$n=rand(1.00,9.99,3);
$nex=range(13,15);
$ans=((($n*10^$nex)*(1.60*10^(-19)))^2)/(2*$U);
$wPlate=switch(rint(2),'positive','negative');@
qu.2.4.uid=c3488c90-0c0b-475d-a1a1-947e25406803@
qu.2.4.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Energy Stored in a Capacitor;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.2.4.weighting=1@
qu.2.4.numbering=alpha@
qu.2.4.part.1.name=sro_id_1@
qu.2.4.part.1.answer.units=@
qu.2.4.part.1.numStyle= scientific  @
qu.2.4.part.1.editing=useHTML@
qu.2.4.part.1.showUnits=false@
qu.2.4.part.1.question=(Unset)@
qu.2.4.part.1.mode=Numeric@
qu.2.4.part.1.grading=exact_sigd@
qu.2.4.part.1.negStyle=both@
qu.2.4.part.1.digit=3@
qu.2.4.part.1.answer.num=$ans@
qu.2.4.question=<p>A spherical capacitor has <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$U</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>J</mi></mrow></mstyle></math>&nbsp;of energy stored inside when <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mstyle></math>&nbsp;electrons are on the<br />&nbsp;$wPlate plate.&nbsp; Calculate the capacitance in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Farads</mi></mrow></mstyle></math>.</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math></span></p>@

qu.2.5.mode=Inline@
qu.2.5.name=Capacitor Geometry - Parallel Plate - Find Potential ~ NG@
qu.2.5.comment=@
qu.2.5.editing=useHTML@
qu.2.5.solution=<p>The relationship between charge, capacitance and voltage for a capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>Q</mi><mrow><mi>V</mi></mrow></mfrac></mrow></mrow></mstyle></math>.&nbsp; We know <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Q</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>e</mi></mrow></mstyle></math>, so we need to find <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>&nbsp;in order to calculate <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>
<p>The capacitance of a parallel-plate capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub><mfrac><mi>A</mi><mrow><mi>d</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Therefore:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$x</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Now, we can calculate <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.2.5.algorithm=$x=rand(10.0,99.9,3);
$y=rand(10.0,99.9,3);
$d=rand(.10,3.0,3);
$n=rand(1,9.99,3);
$nex=range(7,10);
$Q=(1.60*10^(-19))*($n*10^($nex));
$C=($x*10^(-2))*($y*10^(-2))*(8.85*10^(-12))/($d*10^(-3));
$ans=$Q/$C;@
qu.2.5.uid=86a6d52a-9cc4-4ad2-9e37-cc40cf6e8d3d@
qu.2.5.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Geometry of a Capacitor;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.2.5.weighting=1@
qu.2.5.numbering=alpha@
qu.2.5.part.1.name=sro_id_1@
qu.2.5.part.1.answer.units=@
qu.2.5.part.1.numStyle= scientific  @
qu.2.5.part.1.editing=useHTML@
qu.2.5.part.1.showUnits=false@
qu.2.5.part.1.question=(Unset)@
qu.2.5.part.1.mode=Numeric@
qu.2.5.part.1.grading=exact_sigd@
qu.2.5.part.1.negStyle=both@
qu.2.5.part.1.digit=3@
qu.2.5.part.1.answer.num=$ans@
qu.2.5.question=<p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mstyle></math>&nbsp;electrons are accumulated on the negative plate of the capacitor in the diagram, what is<br />the potential difference between the plates, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>?&nbsp;</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="500" height="560"><param name="image" value="__BASE_URI__img/Capacitance/Capacitance-ParallelPlate/Diagram.png" /><param name="size" value="3" /><param name="label.1.x" value="280" /><param name="label.1.y" value="20" /><param name="label.1.text" value="$d mm" /><param name="label.2.x" value="130" /><param name="label.2.y" value="385" /><param name="label.2.text" value="$x cm" /><param name="label.3.x" value="305" /><param name="label.3.y" value="480" /><param name="label.3.text" value="$y cm" /></applet></p><p align="center">&nbsp;</p><p align="center">&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></span></p>@

qu.2.6.mode=Inline@
qu.2.6.name=Simple Capacitance - Find Electrons ~ NG@
qu.2.6.comment=@
qu.2.6.editing=useHTML@
qu.2.6.solution=<p>The relationship between charge, potential difference and capacitance is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>Q</mi><mrow><mi>V</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>.&nbsp; We can then use <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Q</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>n</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>e</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.2.6.algorithm=$C=rand(1.00,9.99,3);
$V=rand(1.00,9.99,3);
$ans=($C*10^(-6))*$V/(1.60*10^(-19));@
qu.2.6.uid=656807d2-c267-49f5-915b-b8ceb74065ef@
qu.2.6.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitance;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.2.6.weighting=1@
qu.2.6.numbering=alpha@
qu.2.6.part.1.name=sro_id_1@
qu.2.6.part.1.answer.units=@
qu.2.6.part.1.numStyle= scientific  @
qu.2.6.part.1.editing=useHTML@
qu.2.6.part.1.showUnits=false@
qu.2.6.part.1.question=(Unset)@
qu.2.6.part.1.mode=Numeric@
qu.2.6.part.1.grading=exact_sigd@
qu.2.6.part.1.negStyle=both@
qu.2.6.part.1.digit=3@
qu.2.6.part.1.answer.num=$ans@
qu.2.6.question=<p><span>A cylindrical capacitor of capacitance&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$C</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;F</mi></mrow></mstyle></math> has developed a potential difference of&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math> between<br />the positive and negative surfaces. How many electrons are there on the negative surface?</span></p><p>&nbsp;</p><p><span><span>&nbsp;</span><1><span>&nbsp;</span></span></p>@

qu.2.7.mode=Inline@
qu.2.7.name=Simple Capacitance - Find V ~ NG@
qu.2.7.comment=@
qu.2.7.editing=useHTML@
qu.2.7.solution=<p>The relationship between charge, potential difference and capacitance is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>Q</mi><mrow><mi>V</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Q</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>e</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.2.7.algorithm=$C=rand(1.00,9.99,3);
$n=rand(1.00,9.99,3);
$nex=range(13,16);
$ans=(($n*10^($nex))*(1.60*10^(-19)))/($C*10^(-6));@
qu.2.7.uid=aa29a9c4-3129-4e3e-838d-e9201e277b53@
qu.2.7.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitance;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.2.7.weighting=1@
qu.2.7.numbering=alpha@
qu.2.7.part.1.name=sro_id_1@
qu.2.7.part.1.answer.units=@
qu.2.7.part.1.numStyle= scientific  @
qu.2.7.part.1.editing=useHTML@
qu.2.7.part.1.showUnits=false@
qu.2.7.part.1.question=(Unset)@
qu.2.7.part.1.mode=Numeric@
qu.2.7.part.1.grading=exact_sigd@
qu.2.7.part.1.negStyle=both@
qu.2.7.part.1.digit=3@
qu.2.7.part.1.answer.num=$ans@
qu.2.7.question=<p><span>A cylindrical capacitor of capacitance&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$C</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;F</mi></mrow></mstyle></math> has accumulated&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mstyle></math>&nbsp;electrons on the negative<br />&nbsp;surface.&nbsp; What is the potential difference between the plates, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>?</span></p><p>&nbsp;</p><p><span><span>&nbsp;</span><1><span>&nbsp;</span></span></p>@

qu.2.8.mode=Inline@
qu.2.8.name=Simple Capacitance - Find C ~ NG@
qu.2.8.comment=@
qu.2.8.editing=useHTML@
qu.2.8.solution=<p>The relationship between charge, potential difference and capacitance is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>Q</mi><mrow><mi>V</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Q</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>e</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.2.8.algorithm=$V=rand(1.00,9.99,3);
$n=rand(1.00,9.99,3);
$nex=range(13,16);
$ans=(($n*10^($nex))*(1.60*10^(-19)))/($V);@
qu.2.8.uid=a6a194a8-4773-405e-adc8-d26feb8bbb15@
qu.2.8.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitance;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.2.8.weighting=1@
qu.2.8.numbering=alpha@
qu.2.8.part.1.name=sro_id_1@
qu.2.8.part.1.answer.units=@
qu.2.8.part.1.numStyle= scientific  @
qu.2.8.part.1.editing=useHTML@
qu.2.8.part.1.showUnits=false@
qu.2.8.part.1.question=(Unset)@
qu.2.8.part.1.mode=Numeric@
qu.2.8.part.1.grading=exact_sigd@
qu.2.8.part.1.negStyle=both@
qu.2.8.part.1.digit=3@
qu.2.8.part.1.answer.num=$ans@
qu.2.8.question=<p><span>A cylindrical capacitor has accumulated&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mstyle></math>&nbsp;electrons on the negative&nbsp;surface, causing a&nbsp;<br />potential difference of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;between the positive and negative surface.&nbsp; What is the capacitance of the&nbsp;<br />capacitor, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math>?</span></p><p>&nbsp;</p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math></span></span></p>@

qu.2.9.mode=Inline@
qu.2.9.name=Capacitor Geometry - Parallel Plate - Find Capacitance ~ NG@
qu.2.9.comment=@
qu.2.9.editing=useHTML@
qu.2.9.solution=<p>The capacitance of a parallel-plate capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub><mfrac><mi>A</mi><mrow><mi>d</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Therefore:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$x</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mstyle></math></p>@
qu.2.9.algorithm=$x=rand(10.0,99.9,3);
$y=rand(10.0,99.9,3);
$d=rand(.10,3.0,3);
$ans=($x*10^(-2))*($y*10^(-2))*(8.85*10^(-12))/($d*10^(-3));@
qu.2.9.uid=cd96d4f8-f0d4-45c3-8bc5-d597907a20f0@
qu.2.9.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Geometry of a Capacitor;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.2.9.weighting=1@
qu.2.9.numbering=alpha@
qu.2.9.part.1.name=sro_id_1@
qu.2.9.part.1.answer.units=@
qu.2.9.part.1.numStyle= scientific  @
qu.2.9.part.1.editing=useHTML@
qu.2.9.part.1.showUnits=false@
qu.2.9.part.1.question=(Unset)@
qu.2.9.part.1.mode=Numeric@
qu.2.9.part.1.grading=exact_sigd@
qu.2.9.part.1.negStyle=both@
qu.2.9.part.1.digit=3@
qu.2.9.part.1.answer.num=$ans@
qu.2.9.question=<p>What is the capacitance of the following capacitor, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math>?&nbsp;</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="500" height="560"><param name="image" value="__BASE_URI__img/Capacitance/Capacitance-ParallelPlate/Diagram.png" /><param name="size" value="3" /><param name="label.1.x" value="280" /><param name="label.1.y" value="20" /><param name="label.1.text" value="$d mm" /><param name="label.2.x" value="130" /><param name="label.2.y" value="385" /><param name="label.2.text" value="$x cm" /><param name="label.3.x" value="305" /><param name="label.3.y" value="480" /><param name="label.3.text" value="$y cm" /></applet></p><p align="center">&nbsp;</p><p align="center">&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math></span></p>@

qu.2.10.mode=Inline@
qu.2.10.name=Capacitors in Series and Parallel 1 ~ NGc@
qu.2.10.comment=@
qu.2.10.editing=useHTML@
qu.2.10.solution=<p>For the bottom arm, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>C</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msub><mi>C</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mn>1</mn><mrow><msub><mi>C</mi><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math>.</p>
<p>The total is then:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>C</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>C</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>C</mi><mrow><mn>3</mn></mrow></msub></mrow></mstyle></math>.</p>@
qu.2.10.algorithm=$mc=maple("(1/C1+1/C2)^(-1)+C3");@
qu.2.10.uid=278271a7-3480-42e2-97f7-b8d2fd038694@
qu.2.10.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitors in Series and Parallel;
  Difficulty=Easy;
  Features=Diagram;
  Features=Algorithmic;
  Features=Algebraic;
@
qu.2.10.weighting=1@
qu.2.10.numbering=alpha@
qu.2.10.part.1.editing=useHTML@
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qu.2.10.part.1.name=sro_id_1@
qu.2.10.part.1.answer=$mc@
qu.2.10.part.1.mode=Formula@
qu.2.10.question=<p align="center"><img alt="" align="middle" width="438" height="400" src="__BASE_URI__img/Capacitance/CapacitorsSeriesParallel1/Diagram.png" /></p><p>&nbsp;</p><p>What is the total capacitance of the circuit between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.2.11.mode=Inline@
qu.2.11.name=Capacitor Geometry - Parallel Plate - Find Separation ~ NG@
qu.2.11.comment=@
qu.2.11.editing=useHTML@
qu.2.11.solution=<p>The capacitance of a parallel-plate capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub><mfrac><mi>A</mi><mrow><mi>d</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Therefore:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$x</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced></mrow><mrow><mi>$C</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nF</mi></mrow></mfrac></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>.</p>
<p>Now, we can calculate <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.2.11.algorithm=$x=rand(10.0,99.9,3);
$y=rand(10.0,99.9,3);
$C=rand(1.00,9.99,3);
$ans=1000*($x*10^(-2))*($y*10^(-2))*(8.85*10^(-12))/($C*10^(-9));@
qu.2.11.uid=e9487df2-8200-46ea-976d-9489615222a1@
qu.2.11.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Geometry of a Capacitor;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.2.11.weighting=1@
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qu.2.11.part.1.answer.units=@
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qu.2.11.part.1.negStyle=both@
qu.2.11.part.1.digit=3@
qu.2.11.part.1.answer.num=$ans@
qu.2.11.question=<p>How far apart, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>mm</mi></mrow></mstyle></math>,&nbsp;must the plates of the capacitor in the diagram be to give it a capacitance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$C</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nF</mi></mrow></mstyle></math>?</p><p align="center">&nbsp;</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="500" height="560"><param name="image" value="__BASE_URI__img/Capacitance/Capacitance-ParallelPlate/Diagram.png" /><param name="size" value="3" /><param name="label.1.x" value="280" /><param name="label.1.y" value="20" /><param name="label.1.text" value="d" /><param name="label.2.x" value="130" /><param name="label.2.y" value="385" /><param name="label.2.text" value="$x cm" /><param name="label.3.x" value="305" /><param name="label.3.y" value="480" /><param name="label.3.text" value="$y cm" /></applet></p><p align="center">&nbsp;</p><p align="center">&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>mm</mi></mrow></mstyle></math></span></p>@

qu.2.12.mode=Inline@
qu.2.12.name=Capacitors in Series and Parallel 2 ~ NGc@
qu.2.12.comment=@
qu.2.12.editing=useHTML@
qu.2.12.solution=<p>For the bottom arm, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>C</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msub><mi>C</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mn>1</mn><mrow><msub><mi>C</mi><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math>.</p>
<p>The total is then:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>C</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>C</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>C</mi><mrow><mn>3</mn></mrow></msub></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>C</mi><mrow><mn>4</mn></mrow></msub></mrow></mstyle></math>.</p>@
qu.2.12.algorithm=$mc=maple("(1/C1+1/C2)^(-1)+C3+C4");@
qu.2.12.uid=cbb0f2d1-022e-4b88-96d8-be7fa3083f90@
qu.2.12.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitors in Series and Parallel;
  Difficulty=Easy;
  Features=Diagram;
  Features=Algorithmic;
  Features=Algebraic;
@
qu.2.12.weighting=1@
qu.2.12.numbering=alpha@
qu.2.12.part.1.editing=useHTML@
qu.2.12.part.1.question=(Unset)@
qu.2.12.part.1.name=sro_id_1@
qu.2.12.part.1.answer=$mc@
qu.2.12.part.1.mode=Formula@
qu.2.12.question=<p align="center"><img alt="" align="middle" width="438" height="400" src="__BASE_URI__img/Capacitance/CapacitorsSeriesParallel2/Diagram.png" /></p><p>&nbsp;</p><p>What is the total capacitance of the circuit between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.2.13.mode=Inline@
qu.2.13.name=Capacitor Geometry - Parallel Plate - Find Charge ~ NG@
qu.2.13.comment=@
qu.2.13.editing=useHTML@
qu.2.13.solution=<p>The relationship between charge, capacitance and voltage for a capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>Q</mi><mrow><mi>V</mi></mrow></mfrac></mrow></mrow></mstyle></math>.&nbsp; We know <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>, so we need to find <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>&nbsp;in order to calculate <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Q</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>
<p>The capacitance of a parallel-plate capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub><mfrac><mi>A</mi><mrow><mi>d</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Therefore:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$x</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Now, we can calculate <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Q</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.2.13.algorithm=$x=rand(10.0,99.9,3);
$y=rand(10.0,99.9,3);
$d=rand(.10,3.0,3);
$V=rand(1,9.99,3);
$C=($x*10^(-2))*($y*10^(-2))*(8.85*10^(-12))/($d*10^(-3));
$ans=$V*$C;@
qu.2.13.uid=8145d163-cab7-468a-8db3-3ede5018527e@
qu.2.13.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Geometry of a Capacitor;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.2.13.part.1.negStyle=both@
qu.2.13.part.1.digit=3@
qu.2.13.part.1.answer.num=$ans@
qu.2.13.question=<p>If the potential difference between the plates of the capacitor in the diagram is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>, what is magnitude<br />of the total charge accumulated on each plate, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>?</p><p align="center">&nbsp;</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="500" height="560"><param name="image" value="__BASE_URI__img/Capacitance/Capacitance-ParallelPlate/Diagram.png" /><param name="size" value="3" /><param name="label.1.x" value="280" /><param name="label.1.y" value="20" /><param name="label.1.text" value="$d mm" /><param name="label.2.x" value="130" /><param name="label.2.y" value="385" /><param name="label.2.text" value="$x cm" /><param name="label.3.x" value="305" /><param name="label.3.y" value="480" /><param name="label.3.text" value="$y cm" /></applet></p><p align="center">&nbsp;</p><p align="center">&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math></span></p>@

qu.2.14.mode=Inline@
qu.2.14.name=Capacitors in Series and Parallel 1 - Numeric ~ NGc@
qu.2.14.comment=@
qu.2.14.editing=useHTML@
qu.2.14.solution=<p>For the bottom arm, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>C</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msub><mi>C</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mn>1</mn><mrow><msub><mi>C</mi><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math>.</p>
<p>The total is then:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>C</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>C</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>C</mi><mrow><mn>3</mn></mrow></msub></mrow></mstyle></math>.</p>@
qu.2.14.algorithm=$C1=rand(1.00,9.99,3);
$C2=rand(1.00,9.99,3);
$C3=rand(1.00,9.99,3);
$C1ex=range(5,7);
$C2ex=range(5,7);
$C3ex=range(5,7);
$mc=maple("((1/($C1*10^(-$C1ex))+1/($C2*10^(-$C2ex)))^(-1)+($C3*10^(-$C3ex)));
");@
qu.2.14.uid=9dfa295b-8a7c-4dcd-8c54-fd08be0074bd@
qu.2.14.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitors in Series and Parallel;
  Difficulty=Easy;
  Features=Diagram;
  Features=Algorithmic;
@
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qu.2.14.part.1.mode=Numeric@
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qu.2.14.part.1.digit=3@
qu.2.14.part.1.answer.num=$mc@
qu.2.14.question=<p align="center"><img alt="" align="middle" width="438" height="400" src="__BASE_URI__img/Capacitance/CapacitorsSeriesParallel1/Diagram.png" /></p><p>&nbsp;</p><p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C1</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$C1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$C1ex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C2</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$C2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$C2ex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C3</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$C3</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$C3ex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>,<br />what is the total capacitance of the circuit between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math></span></p>@

qu.2.15.mode=Inline@
qu.2.15.name=Capacitors in Series and Parallel 2 - Numeric ~ NGc@
qu.2.15.comment=@
qu.2.15.editing=useHTML@
qu.2.15.solution=<p>For the bottom arm, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>C</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msub><mi>C</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mn>1</mn><mrow><msub><mi>C</mi><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math>.</p>
<p>The total is then:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>C</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>C</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>C</mi><mrow><mn>3</mn></mrow></msub></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>C</mi><mrow><mn>4</mn></mrow></msub></mrow></mstyle></math>.</p>@
qu.2.15.algorithm=$C1=rand(1.00,9.99,3);
$C2=rand(1.00,9.99,3);
$C3=rand(1.00,9.99,3);
$C4=rand(1.00,9.99,3);
$C1ex=range(5,7);
$C2ex=range(5,7);
$C3ex=range(5,7);
$C4ex=range(5,7);
$mc=maple("((1/($C1*10^(-$C1ex))+1/($C2*10^(-$C2ex)))^(-1)+($C3*10^(-$C3ex))+($C4*10^(-$C4ex)));
");@
qu.2.15.uid=253d2a79-1a1c-44ef-b150-a3c883ac998c@
qu.2.15.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitors in Series and Parallel;
  Difficulty=Easy;
  Features=Diagram;
  Features=Algorithmic;
@
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qu.2.15.part.1.numStyle= scientific  @
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qu.2.15.part.1.showUnits=false@
qu.2.15.part.1.question=(Unset)@
qu.2.15.part.1.mode=Numeric@
qu.2.15.part.1.grading=exact_sigd@
qu.2.15.part.1.negStyle=both@
qu.2.15.part.1.digit=3@
qu.2.15.part.1.answer.num=$mc@
qu.2.15.question=<p align="center"><img alt="" align="middle" width="438" height="400" src="__BASE_URI__img/Capacitance/CapacitorsSeriesParallel2/Diagram.png" /></p><p>&nbsp;</p><p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C1</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$C1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$C1ex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C2</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$C2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$C2ex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>,&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C3</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$C3</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$C3ex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math><br />and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C4</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$C4</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$C4ex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>, what is the total capacitance of the circuit between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;</span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math></p>@

qu.2.16.mode=Inline@
qu.2.16.name=Capacitance - Coaxial - Find C ~ NGc@
qu.2.16.comment=@
qu.2.16.editing=useHTML@
qu.2.16.solution=<p>The capacitance per unit length for a cylindrical capacitor is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>C</mi><mrow><mi>L</mi></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mn>2</mn><mrow><mi>&pi;</mi></mrow><mrow><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub></mrow></mrow><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><msub><mi>r</mi><mrow><mi>out</mi></mrow></msub><mrow><msub><mi>r</mi><mrow><mi>inner</mi></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Therefore:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>L</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfrac><mrow><mn>2</mn><mrow><mi>&pi;</mi></mrow><mrow><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub></mrow></mrow><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><msub><mi>r</mi><mrow><mi>out</mi></mrow></msub></mrow><mrow><msub><mi>r</mi><mrow><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>in</mo></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfrac></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfrac><mrow><mn>2</mn><mrow><mi>&pi;</mi></mrow><mrow><msub><mi>&epsilon;</mi><mrow><mn>0</mn></mrow></msub></mrow></mrow><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$rout</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi>$rin</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mfrac></mrow></mstyle></math></p>@
qu.2.16.algorithm=$rin=rand(0.2,15,3);
$rout=rand($rin,25,3);
$L=rand(1.00,9.99,3);
$mc=maple("evalf($L*10^(-2)*2*Pi*8.854187817*10^(-12)/ln($rout/$rin));
");@
qu.2.16.uid=2b6b6dc7-33a6-4015-84f9-3e859760bcf4@
qu.2.16.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Capacitance;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.2.16.weighting=1@
qu.2.16.numbering=alpha@
qu.2.16.part.1.name=sro_id_1@
qu.2.16.part.1.answer.units=@
qu.2.16.part.1.numStyle= scientific  @
qu.2.16.part.1.editing=useHTML@
qu.2.16.part.1.showUnits=false@
qu.2.16.part.1.question=(Unset)@
qu.2.16.part.1.mode=Numeric@
qu.2.16.part.1.grading=exact_sigd@
qu.2.16.part.1.negStyle=both@
qu.2.16.part.1.digit=3@
qu.2.16.part.1.answer.num=$mc@
qu.2.16.question=<p>A cylindrical capacitor has inner and outer radii as labelled in following diagram.</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="400" height="420"><param name="image" value="__BASE_URI__img/Capacitance/Capacitance-Coaxial/Diagram.png" /><param name="size" value="4" /><param name="label.1.x" value="83" /><param name="label.1.y" value="24" /><param name="label.1.text" value="$rout mm" /><param name="label.2.x" value="315" /><param name="label.2.y" value="42" /><param name="label.2.text" value="$rin mm" /><param name="label.3.x" value="85" /><param name="label.3.y" value="150" /><param name="label.3.text" value="+D" /><param name="label.4.x" value="310" /><param name="label.4.y" value="150" /><param name="label.4.text" value="-D" /></applet></p><p>Assuming that the surface charge densities are&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>D</mi></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>D</mi></mrow></mstyle></math>, calculate<br />the capacitance for a section of&nbsp;length&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>of the capacitor, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math>.</p><p><span>&nbsp;</span><1><span>&nbsp;</span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi></mrow></mstyle></math></p>@

qu.2.17.mode=Inline@
qu.2.17.name=Energy Stored in Capacitor - Find Energy ~ NG@
qu.2.17.comment=@
qu.2.17.editing=useHTML@
qu.2.17.solution=<p>The energy stored in a capacitor can be expressed as:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>U</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msup><mi>Q</mi><mrow><mn>2</mn></mrow></msup><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>C</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Q</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mfenced><mi>e</mi></mrow></mstyle></math>.</p>@
qu.2.17.algorithm=$C=rand(1.00,9.99,3);
$Cex=range(5,9);
$n=rand(1.00,9.99,3);
$nex=range(13,15);
$ans=((($n*10^$nex)*(1.60*10^(-19)))^2)/(2*($C*10^(-$Cex)));
$wPlate=switch(rint(2),'positive','negative');@
qu.2.17.uid=c6ce2a95-3626-45e7-b46e-a17f2f4fe8b3@
qu.2.17.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Energy Stored in a Capacitor;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.2.17.weighting=1@
qu.2.17.numbering=alpha@
qu.2.17.part.1.name=sro_id_1@
qu.2.17.part.1.answer.units=@
qu.2.17.part.1.numStyle= scientific  @
qu.2.17.part.1.editing=useHTML@
qu.2.17.part.1.showUnits=false@
qu.2.17.part.1.question=(Unset)@
qu.2.17.part.1.mode=Numeric@
qu.2.17.part.1.grading=exact_sigd@
qu.2.17.part.1.negStyle=both@
qu.2.17.part.1.digit=3@
qu.2.17.part.1.answer.num=$ans@
qu.2.17.question=<p>A spherical capacitor has&nbsp;a capacitance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$C</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Cex</mi></mrow></msup><mi>F</mi></mrow></mstyle></math>.&nbsp; When <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$nex</mi></mrow></msup></mrow></mstyle></math>&nbsp;electrons are on&nbsp;<br />the&nbsp;$wPlate plate,&nbsp;how much energy is stored in the capacitor,&nbsp;in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>J</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>J</mi></mrow></mstyle></math></span></p>@

qu.3.topic=Electric Fields@

qu.3.1.mode=Inline@
qu.3.1.name=Infinite Parallel Plates - Find Separation ~ NGc@
qu.3.1.comment=@
qu.3.1.editing=useHTML@
qu.3.1.solution=@
qu.3.1.algorithm=$potGen=rand(10,100,3);
$x=rand(2,15,3);
$EGen=sig(3,$potGen/($x/100));
$pot=sig(3,$EGen*($x/100));
$idx=rint(2);
$dir=switch($idx,1,-1);
$E=sig(3,$EGen*$dir);
$correctPlate=switch($idx,"A","B");
$wrongPlate=switch($idx,"B","A");
$mc=$x;@
qu.3.1.uid=1994cbfd-b267-4fc9-a8b7-19b4a6cad061@
qu.3.1.info=  Course=Introductory Electricity and Magnetism;
  Topic=Electric Potential Between Infinite Parallel Plates;
  Author=Aron Pasieka;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
qu.3.1.weighting=1@
qu.3.1.numbering=alpha@
qu.3.1.part.1.name=sro_id_1@
qu.3.1.part.1.answer.units=@
qu.3.1.part.1.numStyle= scientific  @
qu.3.1.part.1.editing=useHTML@
qu.3.1.part.1.showUnits=false@
qu.3.1.part.1.question=(Unset)@
qu.3.1.part.1.mode=Numeric@
qu.3.1.part.1.grading=exact_sigd@
qu.3.1.part.1.negStyle=both@
qu.3.1.part.1.digit=3@
qu.3.1.part.1.answer.num=$mc@
qu.3.1.question=<p>The magnitude of the potential difference between two infinite<font size="2"> parallel</font> plates is $pot V. The electric field&nbsp;<br />between the plates is measured to be $E V/m <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mi>x</mi><mi>&#x005e;</mi></mover></mrow></mstyle></math>.</p><p align="center">&nbsp;</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="400" height="360"><param name="image" value="__BASE_URI__img/ElectricFields/InfiniteParallelPlates/Diagram.png" /><param name="size" value="1" /><param name="label.1.x" value="295" /><param name="label.1.y" value="12" /><param name="label.1.text" value="x" /></applet>&nbsp;</p><p>&nbsp;</p><p>What is the separation of the plates, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;</span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math></p>@

qu.3.2.mode=Inline@
qu.3.2.name=Infinite Parallel Plates - Magnitude of Potential Difference ~ NGc@
qu.3.2.comment=@
qu.3.2.editing=useHTML@
qu.3.2.solution=@
qu.3.2.algorithm=$potGen=rand(10,100,3);
$x=rand(2,15,3);
$EGen=sig(3,$potGen/($x/100));
$pot=sig(3,$EGen*($x/100));
$idx=rint(2);
$dir=switch($idx,1,-1);
$E=sig(3,$EGen*$dir);
$correctPlate=switch($idx,"A","B");
$wrongPlate=switch($idx,"B","A");
$mc=$pot;@
qu.3.2.uid=ee30cef1-0ae4-41a7-9d54-76de4118bd5b@
qu.3.2.info=  Course=Introductory Electricity and Magnetism;
  Topic=Electric Potential Between Infinite Parallel Plates;
  Author=Aron Pasieka;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
qu.3.2.weighting=1@
qu.3.2.numbering=alpha@
qu.3.2.part.1.name=sro_id_1@
qu.3.2.part.1.answer.units=@
qu.3.2.part.1.numStyle= scientific  @
qu.3.2.part.1.editing=useHTML@
qu.3.2.part.1.showUnits=false@
qu.3.2.part.1.question=(Unset)@
qu.3.2.part.1.mode=Numeric@
qu.3.2.part.1.grading=exact_sigd@
qu.3.2.part.1.negStyle=both@
qu.3.2.part.1.digit=3@
qu.3.2.part.1.answer.num=$mc@
qu.3.2.question=<p>Two infinite<font size="2"> parallel</font> plates are separated by a distance $x cm . The electric field between the plates is&nbsp;<br />measured to be $E V/m <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mi>x</mi><mi>&#x005e;</mi></mover></mrow></mstyle></math>.</p><p align="center">&nbsp;</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="400" height="360"><param name="image" value="__BASE_URI__img/ElectricFields/InfiniteParallelPlates/Diagram.png" /><param name="size" value="1" /><param name="label.1.x" value="295" /><param name="label.1.y" value="12" /><param name="label.1.text" value="$x cm" /></applet>&nbsp;</p><p>&nbsp;</p><p>What is the magnitude of the potential difference between the plates, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;</span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></p>@

qu.3.3.mode=Inline@
qu.3.3.name=Infinite Parallel Plates - Find Field Magnitude ~ NGc@
qu.3.3.comment=@
qu.3.3.editing=useHTML@
qu.3.3.solution=@
qu.3.3.algorithm=$potGen=rand(10,100,3);
$x=rand(2,15,3);
$EGen=sig(3,$potGen/($x/100));
$pot=sig(3,$EGen*($x/100));
$idx=rint(2);
$dir=switch($idx,1,-1);
$E=sig(3,$EGen*$dir);
$correctPlate=switch($idx,"A","B");
$wrongPlate=switch($idx,"B","A");
$mc=abs($E);@
qu.3.3.uid=4ff43e2f-b9de-44a0-8d5a-fdc5f3baf51c@
qu.3.3.info=  Course=Introductory Electricity and Magnetism;
  Topic=Electric Potential Between Infinite Parallel Plates;
  Author=Aron Pasieka;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
qu.3.3.weighting=1@
qu.3.3.numbering=alpha@
qu.3.3.part.1.name=sro_id_1@
qu.3.3.part.1.answer.units=@
qu.3.3.part.1.numStyle= scientific  @
qu.3.3.part.1.editing=useHTML@
qu.3.3.part.1.showUnits=false@
qu.3.3.part.1.question=(Unset)@
qu.3.3.part.1.mode=Numeric@
qu.3.3.part.1.grading=exact_sigd@
qu.3.3.part.1.negStyle=both@
qu.3.3.part.1.digit=3@
qu.3.3.part.1.answer.num=$mc@
qu.3.3.question=<p>The magnitude of the potential difference between two infinite<font size="2"> parallel</font> plates separated by $x cm&nbsp;is $pot V.&nbsp;</p><p align="center"><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="400" height="360"><param name="image" value="__BASE_URI__img/ElectricFields/InfiniteParallelPlates/Diagram.png" /><param name="size" value="1" /><param name="label.1.x" value="295" /><param name="label.1.y" value="12" /><param name="label.1.text" value="$x cm" /></applet>&nbsp;</p><p>&nbsp;</p><p>What is the magnitude of the electric field between the plates, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math></span></p>@

qu.4.topic=Charge in B-Field@

qu.4.1.mode=Inline@
qu.4.1.name=Charged Particle in Magnetic Field - Find Mass ~ NG@
qu.4.1.comment=@
qu.4.1.editing=useHTML@
qu.4.1.solution=<p>If a charge is experiencing circular motion due solely to a magnetic field, then the magnitude of the magnetic field must equal the magnitude of the centripetal force:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='|' close='|' separators=','><mrow><mi>q</mi></mrow></mfenced><mi>vB</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msup><mi>mv</mi><mrow><mn>2</mn></mrow></msup><mrow><mi>R</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>q</mi></mrow></mstyle></math>, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>v</mi></mrow></mstyle></math>, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>.</p>@
qu.4.1.algorithm=$R=rand(10.0,19.9,3);
$q=rand(1.00,9.99,3);
$qex=range(10,15);
$B=rand(0.1,0.999,3);
$v=rand(1.00,9.99,3);
$vex=range(3,5);
$ans=($R*10^(-2))*($q*10^(-$qex))*$B/($v*10^($vex));@
qu.4.1.uid=7ec4777c-886c-4800-b430-d9f4900c10c7@
qu.4.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Charged Particle in a Magnetic Field;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.4.1.weighting=1@
qu.4.1.numbering=alpha@
qu.4.1.part.1.name=sro_id_1@
qu.4.1.part.1.answer.units=@
qu.4.1.part.1.numStyle= scientific  @
qu.4.1.part.1.editing=useHTML@
qu.4.1.part.1.showUnits=false@
qu.4.1.part.1.question=(Unset)@
qu.4.1.part.1.mode=Numeric@
qu.4.1.part.1.grading=exact_sigd@
qu.4.1.part.1.negStyle=both@
qu.4.1.part.1.digit=3@
qu.4.1.part.1.answer.num=$ans@
qu.4.1.question=<p>A charged particle, moving at a speed&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup></mrow><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>,&nbsp;is experiencing circular motion in a magnetic&nbsp;<br />field of strength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$B</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>T</mi></mrow></mstyle></math>.&nbsp; If the particle has a charge of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$q</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$qex</mi></mrow></msup><mi>C</mi></mrow></mstyle></math>&nbsp;and the radius of its motion is&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$R</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>, what is the mass of the particle, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>kg</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>kg</mi></mrow></mstyle></math></span></p>@

qu.4.2.mode=Inline@
qu.4.2.name=Charged Particle in Magnetic Field - Find Field ~ NG@
qu.4.2.comment=@
qu.4.2.editing=useHTML@
qu.4.2.solution=<p>If a charge is experiencing circular motion due solely to a magnetic field, then the magnitude of the magnetic field must equal the magnitude of the centripetal force:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='|' close='|' separators=','><mrow><mi>q</mi></mrow></mfenced><mi>vB</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msup><mi>mv</mi><mrow><mn>2</mn></mrow></msup><mrow><mi>R</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>q</mi></mrow></mstyle></math>, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>v</mi></mrow></mstyle></math>, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>.</p>@
qu.4.2.algorithm=$q=rand(1.00,9.99,3);
$qex=range(10,15);
$R=rand(0.1,0.999,3);
$v=rand(1.00,9.99,3);
$vex=range(3,5);
$m=rand(1.00,9.99,3);
$mex=range(10,15);
$B=($m*10^(-$mex))*($v*10^(-$vex))/(($q*10^(-$qex))*($R/100));@
qu.4.2.uid=d4b254cd-a779-41cd-a910-21e8ca65452a@
qu.4.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Charged Particle in a Magnetic Field;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.4.2.weighting=1@
qu.4.2.numbering=alpha@
qu.4.2.part.1.name=sro_id_1@
qu.4.2.part.1.answer.units=@
qu.4.2.part.1.numStyle= scientific  @
qu.4.2.part.1.editing=useHTML@
qu.4.2.part.1.showUnits=false@
qu.4.2.part.1.question=(Unset)@
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qu.4.2.part.1.grading=exact_sigd@
qu.4.2.part.1.negStyle=both@
qu.4.2.part.1.digit=3@
qu.4.2.part.1.answer.num=$ans@
qu.4.2.question=<p>A charged particle, moving at a speed&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup></mrow><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>,&nbsp;is experiencing circular motion, with radius&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$R</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>,&nbsp;in a magnetic&nbsp;field.&nbsp; If the particle has a charge of&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$qex</mi></mrow></msup><mi>C</mi></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>&nbsp;and mass&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$mex</mi></mrow></msup><mi>kg</mi></mrow></mstyle></math>, what is magnitude of the magnetic field, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>T</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>T</mi></mrow></mstyle></math></span></p>@

qu.4.3.mode=Inline@
qu.4.3.name=Force on Current Carrying Wire - Max Force ~ NG@
qu.4.3.comment=@
qu.4.3.editing=useHTML@
qu.4.3.solution=<p>The force due to a magnetic field on a current carrying wire is given by:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mover><mi>F</mi><mi>&rarr;</mi></mover></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>I</mi><mrow><mover><mrow><mi>l</mi></mrow><mi>&rarr;</mi></mover></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&times;</mo></mrow><mrow><mover><mrow><mi>B</mi></mrow><mi>&rarr;</mi></mover></mrow></mrow></mstyle></math>.</p>
<p>This force is at a maximum when the direction of the current flow is perpendicular to the magnetic field, so that:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>F</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>IlB</mi></mrow></mstyle></math>.</p>
<p>We are given the current, magnetic field and the length of the wire.</p>@
qu.4.3.algorithm=$I=rand(1.00,9.99,3);
$B=rand(0.1,0.999,3);
$l=rand(2,7,3);
$ans=($l*10^(-2))*$B*$I;@
qu.4.3.uid=8507b3d7-a64c-40a0-b601-4659310f7b6b@
qu.4.3.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Force on Current Carrying Wire in Magnetic Field;
  Difficulty=Easy;
  Features=Algorithmic;
@
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qu.4.3.part.1.digit=3@
qu.4.3.part.1.answer.num=$ans@
qu.4.3.question=<p>What is the maximum force, in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Newtons</mi></mrow></mstyle></math>,&nbsp;that a <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$B</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>T</mi></mrow></mstyle></math>&nbsp;magnetic field can cause on a wire of length <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$l</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>&nbsp;that&nbsp;is&nbsp;carrying<br />a current of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>N</mi></mrow></mstyle></math></span></p>@

qu.4.4.mode=Inline@
qu.4.4.name=Charged Particle in Magnetic Field - Find Radius  ~ NG@
qu.4.4.comment=@
qu.4.4.editing=useHTML@
qu.4.4.solution=<p>If a charge is experiencing circular motion due solely to a magnetic field, then the magnitude of the magnetic field must equal the magnitude of the centripetal force:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='|' close='|' separators=','><mrow><mi>q</mi></mrow></mfenced><mi>vB</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><msup><mi>mv</mi><mrow><mn>2</mn></mrow></msup><mrow><mi>R</mi></mrow></mfrac></mrow></mstyle></math>.</p>
<p>We are given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>q</mi></mrow></mstyle></math>, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>v</mi></mrow></mstyle></math>,&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>.</p>@
qu.4.4.algorithm=$q=rand(1.00,9.99,3);
$qex=range(10,15);
$B=rand(0.1,0.999,3);
$v=rand(1.00,9.99,3);
$vex=range(3,5);
$m=rand(1.00,9.99,3);
$mex=range(10,15);
$R=(100*$m*10^(-$mex))*($v*10^(-$vex))/(($q*10^(-$qex))*$B);@
qu.4.4.uid=40344c39-32a4-49fc-975c-e7211f7ce6b8@
qu.4.4.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Charged Particle in a Magnetic Field;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.4.4.weighting=1@
qu.4.4.numbering=alpha@
qu.4.4.part.1.name=sro_id_1@
qu.4.4.part.1.answer.units=@
qu.4.4.part.1.numStyle= scientific  @
qu.4.4.part.1.editing=useHTML@
qu.4.4.part.1.showUnits=false@
qu.4.4.part.1.question=(Unset)@
qu.4.4.part.1.mode=Numeric@
qu.4.4.part.1.grading=exact_sigd@
qu.4.4.part.1.negStyle=both@
qu.4.4.part.1.digit=3@
qu.4.4.part.1.answer.num=$ans@
qu.4.4.question=<p>A charged particle, moving at a speed&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup></mrow><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>,&nbsp;is experiencing circular motion in a magnetic&nbsp;<br />field of strength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$B</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>T</mi></mrow></mstyle></math>.&nbsp; If the particle has a charge of&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$qex</mi></mrow></msup><mi>C</mi></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>&nbsp;and mass <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$mex</mi></mrow></msup><mi>kg</mi></mrow></mstyle></math>,<br />what is radius of its motion, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math></span></p>@

qu.5.topic=Circuits@

qu.5.1.mode=Inline@
qu.5.1.name=Resistors in Series and Parallel 1 - Numeric ~ NGc@
qu.5.1.comment=@
qu.5.1.editing=useHTML@
qu.5.1.solution=<p>For the bottom branch, the equivalent resistance is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>R</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>R</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>R</mi><mrow><mn>2</mn></mrow></msub></mrow></mstyle></math>.</p>
<p>Therefore,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>R</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mi>eq</mi></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mn>3</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math>.</p>@
qu.5.1.algorithm=$R1=rand(1.00,100,3);
$R2=rand(1.00,100,3);
$R3=rand(1.00,100,3);
$mc=1/((1/($R1+$R2))+(1/$R3));@
qu.5.1.uid=7c0ad3a6-478b-4b84-8446-49216b14cb5c@
qu.5.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Resistors in Series and Parallel;
  Difficulty=Easy;
  Features=Diagram;
@
qu.5.1.weighting=1@
qu.5.1.numbering=alpha@
qu.5.1.part.1.name=sro_id_1@
qu.5.1.part.1.answer.units=@
qu.5.1.part.1.numStyle= scientific  @
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qu.5.1.part.1.grading=exact_sigd@
qu.5.1.part.1.negStyle=both@
qu.5.1.part.1.digit=3@
qu.5.1.part.1.answer.num=$mc@
qu.5.1.question=<p align="center"><img alt="" align="middle" width="561" height="500" src="__BASE_URI__img/Resistors/ResistorsInSeriesAndParallel1/Diagram.png" /></p><p>&nbsp;</p><p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R1</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$R1</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mi>&Omega;</mi></mrow></mstyle></math>,&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R2</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$R2</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&Omega;</mi></mrow></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R3</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$R3</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&Omega;</mi></mrow></mstyle></math>, what is the total resistance of the circuit between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Omega;</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;</span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Omega;</mi></mrow></mstyle></math></p>@

qu.5.2.mode=Inline@
qu.5.2.name=Battery - Terminal Voltage 2 - Find V_term ~ NG@
qu.5.2.comment=@
qu.5.2.editing=useHTML@
qu.5.2.solution=<p>The terminal voltage is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>@
qu.5.2.algorithm=$r=rand(1.00,9.99,3);
$I=rand(0.300,0.999,3);
$V=rand(10.0,19.9,3);
$ans=$V+$I*$r;@
qu.5.2.uid=3d00bb9f-ace7-47b8-ad81-8656df86ecd0@
qu.5.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Terminal Voltage;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.5.2.part.1.question=(Unset)@
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qu.5.2.part.1.grading=exact_sigd@
qu.5.2.part.1.negStyle=both@
qu.5.2.part.1.digit=3@
qu.5.2.part.1.answer.num=$ans@
qu.5.2.question=<p><img alt="" align="middle" width="609" height="150" src="__BASE_URI__img/EMF/Battery-Terminal-Voltage-2/Diagram.png" /></p><p><span><br />A battery with internal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;and internal resistance <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&Omega;</mi></mrow></mrow></mstyle></math>&nbsp;has a current&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>&nbsp;passing<br />&nbsp;through it in the direction indicated.&nbsp; What is the terminal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub></mrow></mstyle></math>&nbsp;of the battery, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Volts</mi></mrow></mstyle></math>?</span></p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></span></span></p>@

qu.5.3.mode=Inline@
qu.5.3.name=Battery - Terminal Voltage 1 - Find Current ~ NG@
qu.5.3.comment=@
qu.5.3.editing=useHTML@
qu.5.3.solution=<p>The terminal voltage is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>@
qu.5.3.algorithm=$V=rand(10.0,19.9,3);
$Vterm=rand(5,($V-0.5),3);
$r=rand(2.0,9.0,3);
$ans=($V-$Vterm)/$r;@
qu.5.3.uid=e7615673-7ebf-44d2-b1b0-a25ec667632c@
qu.5.3.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Terminal Voltage;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.5.3.question=<p><img alt="" align="middle" width="609" height="150" src="__BASE_URI__img/EMF/Battery-Terminal-Voltage-1/Diagram.png" /></p><p><span><br />A battery with internal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;and terminal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$Vterm</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;has a current&nbsp;passing<br />&nbsp;through it in the direction indicated.&nbsp; If the internal resistance of the battery is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&Omega;</mi></mrow></mrow></mstyle></math>, what is the<br />&nbsp;magnitude of the current, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Amperes</mi></mrow></mstyle></math>?</span></p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math></span></span></p>@

qu.5.4.mode=Inline@
qu.5.4.name=Charging Battery - Find Voltage  ~ NG@
qu.5.4.comment=@
qu.5.4.editing=useHTML@
qu.5.4.solution=<p>The average power during charging would be:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>P</mi><mrow><mi>av</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>I</mi><mrow><mi>av</mi></mrow></msub><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>
<p>The total energy used is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>P</mi><mrow><mi>av</mi></mrow></msub><mi>&Delta;t</mi></mrow></mstyle></math></p>
<p>Thus,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$cap</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mn>4</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>J</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$t</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.5.4.algorithm=$cap=rand(1.00,3.00,3);
$I=rand(400,510,3);
$t=rand(30.0,90.0,3);
$ans=($cap*10^(4))/(($t*60)*$I/1000);@
qu.5.4.uid=3e71eba3-7134-4c0b-bd4c-bf08ea2da4ba@
qu.5.4.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Power Consumption;
  Difficulty=Medium;
  Features=Algorithmic;
@
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qu.5.4.part.1.digit=3@
qu.5.4.part.1.answer.num=$ans@
qu.5.4.question=<p>A particular phone battery has a capacity of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$cap</mi></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mn>4</mn></mrow></msup><mi>J</mi></mrow></mstyle></math>.&nbsp; If&nbsp;completely charging it from empty takes&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$t</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>min</mi></mrow></mstyle></math>&nbsp;and draws an average&nbsp;current&nbsp;of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mstyle></math>,&nbsp;what is the voltage applied across the terminals of&nbsp;<br />the&nbsp;battery?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></span></p>@

qu.5.5.mode=Inline@
qu.5.5.name=Power Used in Charging - Find Current ~ NG@
qu.5.5.comment=@
qu.5.5.editing=useHTML@
qu.5.5.solution=<p>The instantaneous power during charging would be:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>P</mi><mrow><mi></mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>I</mi><mrow><mi></mi></mrow></msub><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;Thus,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$P</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>W</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.5.5.algorithm=$P=rand(2.4,2.7,3);
$V=rand(4.60,5.19,3);
$ans=1000*$P/$V;@
qu.5.5.uid=a2d74015-5aca-42b5-987a-3421e41f2e17@
qu.5.5.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Power Usage;
  Difficulty=Easy;
  Features=Algorithmic;
@
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qu.5.5.part.1.showUnits=false@
qu.5.5.part.1.question=(Unset)@
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qu.5.5.part.1.negStyle=both@
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qu.5.5.part.1.answer.num=$ans@
qu.5.5.question=<p>Charging an iPhone over a USB cable draws roughly <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$P</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>W</mi></mrow></mstyle></math>.&nbsp; The <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;line in the USB cable that&nbsp;<br />provides the current, is measured in a particular case to be at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>.&nbsp; What current is being drawn by&nbsp;<br />the phone?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>mA</mi></mrow></mstyle></math></span></p>@

qu.5.6.mode=Inline@
qu.5.6.name=Battery - Terminal Voltage 1 - Find V_term ~ NG@
qu.5.6.comment=@
qu.5.6.editing=useHTML@
qu.5.6.solution=<p>The terminal voltage is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>@
qu.5.6.algorithm=$r=rand(1.00,9.99,3);
$I=rand(0.300,0.999,3);
$V=rand(10.0,19.9,3);
$ans=$V-$I*$r;@
qu.5.6.uid=a6b99a00-c3e7-4e36-875f-1ebc6279a1e6@
qu.5.6.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Terminal Voltage;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
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qu.5.6.part.1.digit=3@
qu.5.6.part.1.answer.num=$ans@
qu.5.6.question=<p><img alt="" align="middle" width="609" height="150" src="__BASE_URI__img/EMF/Battery-Terminal-Voltage-1/Diagram.png" /></p><p><span><br />A battery with internal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;and internal resistance <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&Omega;</mi></mrow></mrow></mstyle></math>&nbsp;has a current&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>&nbsp;passing<br />&nbsp;through it in the direction indicated.&nbsp; What is the terminal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub></mrow></mstyle></math>&nbsp;of the battery, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Volts</mi></mrow></mstyle></math>?</span></p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></span></span></p>@

qu.5.7.mode=Inline@
qu.5.7.name=Resistors in Series and Parallel 1 ~ NGc@
qu.5.7.comment=@
qu.5.7.editing=useHTML@
qu.5.7.solution=<p>For the bottom branch, the equivalent resistance is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>R</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>R</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>R</mi><mrow><mn>2</mn></mrow></msub></mrow></mstyle></math>.</p>
<p>Therefore,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>R</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mi>eq</mi></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mn>3</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math>.</p>@
qu.5.7.algorithm=$mc=1/((1/(R1+R2))+(1/R3));@
qu.5.7.uid=561b5314-0db3-4263-873b-5218648bb399@
qu.5.7.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Resistors in Series and Parallel;
  Difficulty=Easy;
  Features=Diagram;
  Features=Algebraic;
@
qu.5.7.weighting=1@
qu.5.7.numbering=alpha@
qu.5.7.part.1.editing=useHTML@
qu.5.7.part.1.question=(Unset)@
qu.5.7.part.1.name=sro_id_1@
qu.5.7.part.1.answer=$mc@
qu.5.7.part.1.mode=Formula@
qu.5.7.question=<p align="center"><img alt="" align="middle" width="561" height="500" src="__BASE_URI__img/Resistors/ResistorsInSeriesAndParallel1/Diagram.png" /></p><p>&nbsp;</p><p>What is the total resistance of the circuit between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.5.8.mode=Inline@
qu.5.8.name=Battery - Terminal Voltage 2 - Find Current ~ NG@
qu.5.8.comment=@
qu.5.8.editing=useHTML@
qu.5.8.solution=<p>The terminal voltage is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>
<p>Thus:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>I</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>V</mi></mrow><mrow><mi>r</mi></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.5.8.algorithm=$Vterm=rand(10.0,19.9,3);
$V=rand(5,($Vterm-0.5),3);
$r=rand(2.0,9.0,3);
$ans=(-$V+$Vterm)/$r;@
qu.5.8.uid=c77fabdc-8c80-4951-90b4-33ace9678e6e@
qu.5.8.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Terminal Voltage;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
qu.5.8.weighting=1@
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qu.5.8.part.1.numStyle= scientific  @
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qu.5.8.part.1.question=(Unset)@
qu.5.8.part.1.mode=Numeric@
qu.5.8.part.1.grading=exact_sigd@
qu.5.8.part.1.negStyle=both@
qu.5.8.part.1.digit=3@
qu.5.8.part.1.answer.num=$ans@
qu.5.8.question=<p><img alt="" align="middle" width="609" height="150" src="__BASE_URI__img/EMF/Battery-Terminal-Voltage-2/Diagram.png" /></p><p><span><br />A battery with internal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;and terminal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$Vterm</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;has a current&nbsp;passing<br />&nbsp;through it in the direction indicated.&nbsp; If the internal resistance of the battery is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&Omega;</mi></mrow></mrow></mstyle></math>, what is the<br />&nbsp;magnitude of the current, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Amperes</mi></mrow></mstyle></math>?</span></p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math></span></span></p>@

qu.5.9.mode=Inline@
qu.5.9.name=Battery - Terminal Voltage 2 - Find r ~ NG@
qu.5.9.comment=@
qu.5.9.editing=useHTML@
qu.5.9.solution=<p>The terminal voltage is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>
<p>Thus:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>V</mi></mrow><mrow><mi>I</mi></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.5.9.algorithm=$I=rand(0.300,0.999,3);
$Vterm=rand(10.0,19.9,3);
$V=rand(5,($Vterm-0.5),3);
$ans=(-$V+$Vterm)/$I;@
qu.5.9.uid=b91e1470-1efd-4267-a4b7-0a52a67d95a8@
qu.5.9.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Terminal Voltage;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
qu.5.9.weighting=1@
qu.5.9.numbering=alpha@
qu.5.9.part.1.name=sro_id_1@
qu.5.9.part.1.answer.units=@
qu.5.9.part.1.numStyle= scientific  @
qu.5.9.part.1.editing=useHTML@
qu.5.9.part.1.showUnits=false@
qu.5.9.part.1.question=(Unset)@
qu.5.9.part.1.mode=Numeric@
qu.5.9.part.1.grading=exact_sigd@
qu.5.9.part.1.negStyle=both@
qu.5.9.part.1.digit=3@
qu.5.9.part.1.answer.num=$ans@
qu.5.9.question=<p><img alt="" align="middle" width="609" height="150" src="__BASE_URI__img/EMF/Battery-Terminal-Voltage-2/Diagram.png" /></p><p><span><br />A battery with internal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;and terminal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$Vterm</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;has a current&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>&nbsp;passing<br />&nbsp;through it in the direction indicated.&nbsp; What is the internal resistance&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi></mrow></mstyle></math>&nbsp;of the battery, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Ohms</mi></mrow></mstyle></math>?</span></p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Omega;</mi></mrow></mstyle></math></span></span></p>@

qu.5.10.mode=Inline@
qu.5.10.name=Resistors in Series and Parallel 2 - Numeric ~ NGc@
qu.5.10.comment=@
qu.5.10.editing=useHTML@
qu.5.10.solution=<p>For the bottom branch, the equivalent resistance is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>R</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>R</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>R</mi><mrow><mn>2</mn></mrow></msub></mrow></mstyle></math>.</p>
<p>Therefore,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>R</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mi>eq</mi></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mn>3</mn></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mn>4</mn></mrow></msub></mrow></mfrac></mrow></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math>.</p>@
qu.5.10.algorithm=$R1=rand(1.00,100,3);
$R2=rand(1.00,100,3);
$R3=rand(1.00,100,3);
$R4=rand(1.00,100,3);
$mc=1/((1/($R1+$R2))+(1/$R3)+(1/$R4));@
qu.5.10.uid=d83beb9f-eedc-43d7-9ea2-29027cf54681@
qu.5.10.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Resistors in Series and Parallel;
  Difficulty=Easy;
  Features=Diagram;
@
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qu.5.10.part.1.answer.num=$mc@
qu.5.10.question=<p align="center"><img alt="" align="middle" width="561" height="500" src="__BASE_URI__img/Resistors/ResistorsInSeriesAndParallel2/Diagram.png" /></p><p>&nbsp;</p><p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R1</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$R1</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mi>&Omega;</mi></mrow></mstyle></math>,&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R2</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$R2</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&Omega;</mi></mrow></mrow></mstyle></math>,&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R3</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$R3</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&Omega;</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R4</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$R4</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&Omega;</mi></mrow></mrow></mstyle></math>, what is the total<br />resistance of the circuit between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Omega;</mi></mrow></mstyle></math>?</p><p><span>&nbsp;</span><1><span>&nbsp;</span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Omega;</mi></mrow></mstyle></math></p>@

qu.5.11.mode=Inline@
qu.5.11.name=Power Used in Charging - Find Voltage ~ NG@
qu.5.11.comment=@
qu.5.11.editing=useHTML@
qu.5.11.solution=<p>The instantaneous power during charging would be:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>P</mi><mrow><mi></mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>I</mi><mrow><mi></mi></mrow></msub><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;Thus,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$P</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>W</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.5.11.algorithm=$P=rand(2.3,2.5,3);
$I=rand(450,520,3);
$ans=(1000*$P)/$I;@
qu.5.11.uid=28dec5c5-4a68-4c2d-a91b-6110ab014153@
qu.5.11.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Power Usage;
  Difficulty=Easy;
  Features=Algorithmic;
@
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qu.5.11.question=<p>The <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;line&nbsp;in a&nbsp;USB cable does not provide exactly <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>, but fluctuates around this value.&nbsp; If , while&nbsp;<br />charging an iPhone over a USB, one measures the power&nbsp;used to be <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$P</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>W</mi></mrow></mstyle></math>, and the current to be<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mstyle></math>,&nbsp;what is the actual voltage provided by the <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;line?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></span></p>@

qu.5.12.mode=Inline@
qu.5.12.name=Battery - Terminal Voltage 1 - Find r ~ NG@
qu.5.12.comment=@
qu.5.12.editing=useHTML@
qu.5.12.solution=<p>The terminal voltage is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>
<p>Thus:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>r</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub></mrow><mrow><mi>I</mi></mrow></mfrac></mrow></mstyle></math></p>@
qu.5.12.algorithm=$I=rand(0.300,0.999,3);
$V=rand(10.0,19.9,3);
$Vterm=rand(5,($V-0.5),3);
$ans=($V-$Vterm)/$I;@
qu.5.12.uid=91b727c5-da2b-42b1-b04e-89fec8fad862@
qu.5.12.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Terminal Voltage;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.5.12.part.1.editing=useHTML@
qu.5.12.part.1.showUnits=false@
qu.5.12.part.1.question=(Unset)@
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qu.5.12.question=<p><img alt="" align="middle" width="609" height="150" src="__BASE_URI__img/EMF/Battery-Terminal-Voltage-1/Diagram.png" /></p><p><span><br />A battery with internal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;and terminal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$Vterm</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;has a current&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>&nbsp;passing<br />&nbsp;through it in the direction indicated.&nbsp; What is the internal resistance&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi></mrow></mstyle></math>&nbsp;of the battery, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Ohms</mi></mrow></mstyle></math>?</span></p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Omega;</mi></mrow></mstyle></math></span></span></p>@

qu.5.13.mode=Inline@
qu.5.13.name=Resistors in Series and Parallel 2 ~ NGc@
qu.5.13.comment=@
qu.5.13.editing=useHTML@
qu.5.13.solution=<p>For the bottom branch, the equivalent resistance is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>R</mi><mrow><mi>eq</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>R</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>R</mi><mrow><mn>2</mn></mrow></msub></mrow></mstyle></math>.</p>
<p>Therefore,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>R</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mi>eq</mi></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mn>3</mn></mrow></msub></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><msub><mi>R</mi><mrow><mn>4</mn></mrow></msub></mrow></mfrac></mrow></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math>.</p>@
qu.5.13.algorithm=$mc=1/((1/(R1+R2))+(1/R3)+(1/R4));@
qu.5.13.uid=3bb32252-9d90-4353-8d32-86c18ecca27a@
qu.5.13.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Resistors in Series and Parallel;
  Difficulty=Easy;
  Features=Diagram;
  Features=Algebraic;
@
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qu.5.13.part.1.answer=$mc@
qu.5.13.part.1.mode=Formula@
qu.5.13.question=<p align="center"><img alt="" align="middle" width="561" height="500" src="__BASE_URI__img/Resistors/ResistorsInSeriesAndParallel2/Diagram.png" /></p><p>&nbsp;</p><p>What is the total resistance of the circuit between <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>B</mi></mrow></mstyle></math>?</p><p><1></p>@

qu.5.14.mode=Inline@
qu.5.14.name=Charging Battery - Find Time ~ NG@
qu.5.14.comment=@
qu.5.14.editing=useHTML@
qu.5.14.solution=<p>The average power during charging would be:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>P</mi><mrow><mi>av</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>I</mi><mrow><mi>av</mi></mrow></msub><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>
<p>The total energy used is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>P</mi><mrow><mi>av</mi></mrow></msub><mi>&Delta;t</mi></mrow></mstyle></math></p>
<p>Thus,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Delta;t</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$cap</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mn>4</mn></mrow></msup><mi>J</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.5.14.algorithm=$cap=rand(1.00,3.00,3);
$V=rand(4.60,5.20,3);
$I=rand(400,510,3);
$ans=($cap*10^(4))/($V*$I/1000);@
qu.5.14.uid=e102ebe5-a8dd-4b78-93ee-aab360ed2f16@
qu.5.14.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Power Consumption;
  Difficulty=Medium;
  Features=Algorithmic;
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qu.5.14.question=<p>A particular phone battery has a capacity of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$cap</mi></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mn>4</mn></mrow></msup><mi>J</mi></mrow></mstyle></math>.&nbsp; If you were to charge it from empty through&nbsp;<br />a&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;USB port and measured the average current to be <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mstyle></math>,&nbsp;how many hours would it take to&nbsp;<br />fully&nbsp;charge?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>h</mi></mrow></mstyle></math></span></p>@

qu.5.15.mode=Inline@
qu.5.15.name=Power Used in Charging - Find Power ~ NG@
qu.5.15.comment=@
qu.5.15.editing=useHTML@
qu.5.15.solution=<p>The instantaneous power during charging would be:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>P</mi><mrow><mi></mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>I</mi><mrow><mi></mi></mrow></msub><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;Thus,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mfenced></mrow></mstyle></math>.</p>@
qu.5.15.algorithm=$I=rand(450,520,3);
$V=rand(4.50,5.20,3);
$ans=($I/1000)*$V;@
qu.5.15.uid=c6f83f50-1fda-468d-883a-1e00362f2505@
qu.5.15.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Power Usage;
  Difficulty=Easy;
  Features=Algorithmic;
@
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qu.5.15.question=<p>The <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;line&nbsp;in a&nbsp;USB cable does not provide exactly <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>, but fluctuates around this value.&nbsp; If , while&nbsp;<br />charging an iPhone over a USB cable, one measures the actual voltage to be <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math> and the current to&nbsp;<br />be<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mstyle></math>,&nbsp;what is the power drawn, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>W</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>W</mi></mrow></mstyle></math></span></p>@

qu.5.16.mode=Inline@
qu.5.16.name=Charging Battery - Find Capacity ~ NG@
qu.5.16.comment=@
qu.5.16.editing=useHTML@
qu.5.16.solution=<p>The average power during charging would be:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>P</mi><mrow><mi>av</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>I</mi><mrow><mi>av</mi></mrow></msub><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>
<p>The total energy used is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>P</mi><mrow><mi>av</mi></mrow></msub><mi>&Delta;t</mi></mrow></mstyle></math></p>
<p>Thus,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$t</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced></mrow></mstyle></math>.</p>@
qu.5.16.algorithm=$t=rand(30,90,3);
$V=rand(4.60,5.20,3);
$I=rand(400,510,3);
$ans=($V*$I/1000)*($t*60);@
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qu.5.16.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Power Consumption;
  Difficulty=Medium;
  Features=Algorithmic;
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qu.5.16.question=<p>If&nbsp;completely charging a particular battery&nbsp;from empty by applying a voltage of&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;for <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$t</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>min</mi></mrow></mstyle></math>&nbsp;drew an&nbsp;<br />average current of<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mA</mi></mrow></mstyle></math>, what is the total capacity of the battery, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>J</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>J</mi></mrow></mstyle></math></span></p>@

qu.5.17.mode=Inline@
qu.5.17.name=Battery - Terminal Voltage 1 - Find EMF ~ NG@
qu.5.17.comment=@
qu.5.17.editing=useHTML@
qu.5.17.solution=<p>The terminal voltage is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>
<p>Thus:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>@
qu.5.17.algorithm=$I=rand(0.300,0.999,3);
$r=rand(2,8,3);
$Vterm=rand(5,15,3);
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qu.5.17.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Terminal Voltage;
  Difficulty=Easy;
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qu.5.17.part.1.digit=3@
qu.5.17.part.1.answer.num=$ans@
qu.5.17.question=<p><img alt="" align="middle" width="609" height="150" src="__BASE_URI__img/EMF/Battery-Terminal-Voltage-1/Diagram.png" /></p><p><span><br />A battery with&nbsp;internal resistance&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi></mrow><mrow><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&Omega;</mi></mrow></mstyle></math>&nbsp;and terminal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$Vterm</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;has a current&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>&nbsp;passing<br />&nbsp;through it in the direction indicated.&nbsp; What is the internal voltage of the battery, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Volts</mi></mrow></mstyle></math>?</span></p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></span></span></p>@

qu.5.18.mode=Inline@
qu.5.18.name=Battery - Terminal Voltage 2 - Find EMF ~ NG@
qu.5.18.comment=@
qu.5.18.editing=useHTML@
qu.5.18.solution=<p>The terminal voltage is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>
<p>Thus:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>V</mi><mrow><mi>AB</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Ir</mi></mrow></mstyle></math>.</p>@
qu.5.18.algorithm=$I=rand(0.300,0.999,3);
$r=rand(2,8,3);
$Vterm=rand(5,15,3);
$V=$Vterm-$r*$I;@
qu.5.18.uid=7b49181e-365b-4915-a758-59f98ca015c7@
qu.5.18.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Terminal Voltage;
  Difficulty=Easy;
  Features=Algorithmic;
  Features=Diagram;
@
qu.5.18.weighting=1@
qu.5.18.numbering=alpha@
qu.5.18.part.1.name=sro_id_1@
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qu.5.18.part.1.editing=useHTML@
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qu.5.18.part.1.question=(Unset)@
qu.5.18.part.1.mode=Numeric@
qu.5.18.part.1.grading=exact_sigd@
qu.5.18.part.1.negStyle=both@
qu.5.18.part.1.digit=3@
qu.5.18.part.1.answer.num=$ans@
qu.5.18.question=<p><img alt="" align="middle" width="609" height="150" src="__BASE_URI__img/EMF/Battery-Terminal-Voltage-2/Diagram.png" /></p><p><span><br />A battery with&nbsp;internal resistance&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi></mrow><mrow><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&Omega;</mi></mrow></mstyle></math>&nbsp;and terminal voltage <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$Vterm</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;has a current&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>&nbsp;passing<br />&nbsp;through it in the direction indicated.&nbsp; What is the internal voltage of the battery, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>Volts</mi></mrow></mstyle></math>?</span></p><p><span><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></span></span></p>@

qu.5.19.mode=Inline@
qu.5.19.name=Charging Battery - Find Current ~ NG@
qu.5.19.comment=@
qu.5.19.editing=useHTML@
qu.5.19.solution=<p>The average power during charging would be:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>P</mi><mrow><mi>av</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>I</mi><mrow><mi>av</mi></mrow></msub><mi>V</mi></mrow></mstyle></math>.</p>
<p>&nbsp;</p>
<p>The total energy used is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>P</mi><mrow><mi>av</mi></mrow></msub><mi>&Delta;t</mi></mrow></mstyle></math></p>
<p>Thus,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>I</mi><mrow><mi>av</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$cap</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mn>4</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>J</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$t</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.5.19.algorithm=$cap=rand(1.00,3.00,3);
$V=rand(4.50,5.20,3);
$t=rand(30.0,90.0,3);
$ans=($cap*10^(4))/(($t*60)*$V);@
qu.5.19.uid=b785000a-3414-4e86-a552-2f0203c25225@
qu.5.19.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Power Consumption;
  Difficulty=Medium;
  Features=Algorithmic;
@
qu.5.19.weighting=1@
qu.5.19.numbering=alpha@
qu.5.19.part.1.name=sro_id_1@
qu.5.19.part.1.answer.units=@
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qu.5.19.part.1.editing=useHTML@
qu.5.19.part.1.showUnits=false@
qu.5.19.part.1.question=(Unset)@
qu.5.19.part.1.mode=Numeric@
qu.5.19.part.1.grading=exact_sigd@
qu.5.19.part.1.negStyle=both@
qu.5.19.part.1.digit=3@
qu.5.19.part.1.answer.num=$ans@
qu.5.19.question=<p>A particular phone battery has a capacity of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$cap</mi></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mn>4</mn></mrow></msup><mi>J</mi></mrow></mstyle></math>.&nbsp; If&nbsp;completely charging it from empty takes&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$t</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>min</mi></mrow></mstyle></math>&nbsp;when a potential difference of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>V</mi></mrow></mstyle></math>&nbsp;is applied,&nbsp;what is the average current passing through&nbsp;<br />the&nbsp;battery during this time, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math></span></p>@

qu.6.topic=Diffraction@

qu.6.1.mode=Inline@
qu.6.1.name=Diffraction Grating - Find Slit Spacing - Dark ~ NG@
qu.6.1.comment=@
qu.6.1.editing=useHTML@
qu.6.1.solution=<p>For a diffraction grating, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.1.algorithm=$m=range(1,4);
$theta=rand(0,20,3);
$lambda=range(100,999);
$ans=($m/2)*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360);@
qu.6.1.uid=d8f58e0e-cc39-4e1d-9a8f-5f7b131f78d5@
qu.6.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.1.weighting=1@
qu.6.1.numbering=alpha@
qu.6.1.part.1.name=sro_id_1@
qu.6.1.part.1.answer.units=@
qu.6.1.part.1.numStyle= scientific  @
qu.6.1.part.1.editing=useHTML@
qu.6.1.part.1.showUnits=false@
qu.6.1.part.1.question=(Unset)@
qu.6.1.part.1.mode=Numeric@
qu.6.1.part.1.grading=exact_sigd@
qu.6.1.part.1.negStyle=both@
qu.6.1.part.1.digit=3@
qu.6.1.part.1.answer.num=$ans@
qu.6.1.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of&nbsp;<br />monochromatic light&nbsp;passes through the grating at normal incidence.&nbsp; If the&nbsp;order-$m dark fringes&nbsp;are&nbsp;<br />visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;for light of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>,&nbsp;what is the slit spacing <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p align="left"><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math></span></p>@

qu.6.2.mode=Inline@
qu.6.2.name=Diffraction Grating - Find Screen Height - Dark ~ NG@
qu.6.2.comment=@
qu.6.2.editing=useHTML@
qu.6.2.solution=<p>For a diffraction grating, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Given the distance from the screen to the grating, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi mathvariant='normal'>y</mi><mrow><mi>$m</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$X</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>m</mi></mrow></mfenced><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.2.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$ans=tan(arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3))))*$X*10^(2);@
qu.6.2.uid=3aa2781a-b18d-468f-9437-dfb4c1817a66@
qu.6.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.2.weighting=1@
qu.6.2.numbering=alpha@
qu.6.2.part.1.name=sro_id_1@
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qu.6.2.part.1.question=(Unset)@
qu.6.2.part.1.mode=Numeric@
qu.6.2.part.1.grading=exact_sigd@
qu.6.2.part.1.negStyle=both@
qu.6.2.part.1.digit=3@
qu.6.2.part.1.answer.num=$ans@
qu.6.2.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If the light&nbsp;incident&nbsp;<br />on the slits is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what distance above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math> would one&nbsp;find&nbsp;the&nbsp;<br />order-$m dark fringes on the screen, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="$X m" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math></span></p>@

qu.6.3.mode=Inline@
qu.6.3.name=Diffraction Grating - Find Screen Height - Bright ~ NG@
qu.6.3.comment=@
qu.6.3.editing=useHTML@
qu.6.3.solution=<p>For a diffraction grating, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Given that the distance to the screen is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$X</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>m</mi></mrow></mstyle></math>, we can find the height of the fringe by:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$X</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>m</mi></mrow></mfenced><mrow><mi>tan</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.3.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$ans=tan(arcsin(($m*$lambda*10^(-9))/($d*10^(-3))))*$X*10^(2);@
qu.6.3.uid=19bc1aa2-5cae-46c0-9194-2f0c170b40c7@
qu.6.3.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.3.weighting=1@
qu.6.3.numbering=alpha@
qu.6.3.part.1.name=sro_id_1@
qu.6.3.part.1.answer.units=@
qu.6.3.part.1.numStyle= scientific  @
qu.6.3.part.1.editing=useHTML@
qu.6.3.part.1.showUnits=false@
qu.6.3.part.1.question=(Unset)@
qu.6.3.part.1.mode=Numeric@
qu.6.3.part.1.grading=exact_sigd@
qu.6.3.part.1.negStyle=both@
qu.6.3.part.1.digit=3@
qu.6.3.part.1.answer.num=$ans@
qu.6.3.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If the light&nbsp;incident&nbsp;<br />on the slits is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what distance above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math> would one&nbsp;find&nbsp;the&nbsp;<br />order-$m bright fringes on the screen, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="$X m" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math></span></p>@

qu.6.4.mode=Inline@
qu.6.4.name=Single Slit Diffraction - Find Angle - Bright ~ NG@
qu.6.4.comment=@
qu.6.4.editing=useHTML@
qu.6.4.solution=<p>For a single slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.4.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$ans=arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3)))*(360/(2*Pi));@
qu.6.4.uid=7c211a13-11a0-48fe-88fb-0ec772a4748f@
qu.6.4.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.4.weighting=1@
qu.6.4.numbering=alpha@
qu.6.4.part.1.name=sro_id_1@
qu.6.4.part.1.answer.units=@
qu.6.4.part.1.numStyle= scientific  @
qu.6.4.part.1.editing=useHTML@
qu.6.4.part.1.showUnits=false@
qu.6.4.part.1.question=(Unset)@
qu.6.4.part.1.mode=Numeric@
qu.6.4.part.1.grading=exact_sigd@
qu.6.4.part.1.negStyle=both@
qu.6.4.part.1.digit=3@
qu.6.4.part.1.answer.num=$ans@
qu.6.4.question=<p>The slit in the diagram&nbsp;is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>. If&nbsp;the light&nbsp;incident on the slit is of&nbsp;<br />wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what angle, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>degrees</mi></mrow></mstyle></math>, would one find&nbsp;the&nbsp;order-$m bright fringes?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi></mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math></span></p>@

qu.6.5.mode=Inline@
qu.6.5.name=Single Slit Diffraction - Find Fringe Order - Bright ~ NG@
qu.6.5.comment=@
qu.6.5.editing=useHTML@
qu.6.5.solution=<p>For a single slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.5.algorithm=$m=range(1,6);
$theta=rand(0,45,3);
$lambda=range(100,999);
$d=sig(3,($m/2)*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360));@
qu.6.5.uid=60e136a6-fee9-4a12-911e-5d57ffe8f366@
qu.6.5.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.5.weighting=1@
qu.6.5.numbering=alpha@
qu.6.5.part.1.name=sro_id_1@
qu.6.5.part.1.answer.units=@
qu.6.5.part.1.numStyle= scientific  @
qu.6.5.part.1.editing=useHTML@
qu.6.5.part.1.showUnits=false@
qu.6.5.part.1.question=(Unset)@
qu.6.5.part.1.mode=Numeric@
qu.6.5.part.1.grading=exact_value@
qu.6.5.part.1.negStyle=both@
qu.6.5.part.1.answer.num=$m@
qu.6.5.question=<p>The slit in the diagram&nbsp;is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi></mrow><mrow><mi></mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mstyle></math>,&nbsp;with <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A&nbsp;beam of&nbsp;monochromatic light&nbsp;of&nbsp;<br />wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>passes through the slit at normal&nbsp;incidence.&nbsp; What order of&nbsp;bright fringes&nbsp;are&nbsp;<br />observed at an angle <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.6.6.mode=Inline@
qu.6.6.name=Single Slit Diffraction - Find Angle - Dark ~ NG@
qu.6.6.comment=@
qu.6.6.editing=useHTML@
qu.6.6.solution=<p>For a single slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.6.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$ans=arcsin(($m*$lambda*10^(-9))/($d*10^(-3)))*(360/(2*Pi));@
qu.6.6.uid=25f71873-9ff8-437c-b028-33f86194dc8f@
qu.6.6.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.6.weighting=1@
qu.6.6.numbering=alpha@
qu.6.6.part.1.name=sro_id_1@
qu.6.6.part.1.answer.units=@
qu.6.6.part.1.numStyle= scientific  @
qu.6.6.part.1.editing=useHTML@
qu.6.6.part.1.showUnits=false@
qu.6.6.part.1.question=(Unset)@
qu.6.6.part.1.mode=Numeric@
qu.6.6.part.1.grading=exact_sigd@
qu.6.6.part.1.negStyle=both@
qu.6.6.part.1.digit=3@
qu.6.6.part.1.answer.num=$ans@
qu.6.6.question=<p>The single slit&nbsp;in the diagram is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>. &nbsp;If&nbsp;the&nbsp;light&nbsp;incident on the slit is of&nbsp;<br />wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what angle, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>degrees</mi></mrow></mstyle></math>, would one find&nbsp;the&nbsp;order-$m dark fringes?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi></mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math></span></p>@

qu.6.7.mode=Inline@
qu.6.7.name=Diffraction Grating - Find Fringe Order - Bright ~ NG@
qu.6.7.comment=@
qu.6.7.editing=useHTML@
qu.6.7.solution=<p>For a diffraction grating, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfrac><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.7.algorithm=$m=range(1,6);
$theta=rand(0,45,3);
$lambda=range(100,999);
$d=sig(3,$m*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360));@
qu.6.7.uid=f00376db-302d-4285-833b-99b3b418d5e8@
qu.6.7.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.6.7.part.1.negStyle=both@
qu.6.7.part.1.answer.num=$m@
qu.6.7.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi></mrow><mrow><mi></mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mstyle></math>,&nbsp;with <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A&nbsp;<br />beam of&nbsp;monochromatic light&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>passes through the grating at normal&nbsp;<br />incidence.&nbsp; What order of&nbsp;bright fringes&nbsp;are observed at an angle <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.6.8.mode=Inline@
qu.6.8.name=Diffraction Grating - Find Fringe Order - Dark ~ NG@
qu.6.8.comment=@
qu.6.8.editing=useHTML@
qu.6.8.solution=<p>For a diffraction grating, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow></mfrac><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.8.algorithm=$m=range(1,6);
$theta=rand(0,45,3);
$lambda=range(100,999);
$d=sig(3,($m/2)*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360));@
qu.6.8.uid=79696a61-54e2-43df-a260-7778dba96425@
qu.6.8.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.6.8.part.1.showUnits=false@
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qu.6.8.part.1.mode=Numeric@
qu.6.8.part.1.grading=exact_value@
qu.6.8.part.1.negStyle=both@
qu.6.8.part.1.answer.num=$m@
qu.6.8.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi></mrow><mrow><mi></mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mstyle></math>,&nbsp;with <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A&nbsp;<br />beam of&nbsp;monochromatic light&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>passes through the grating at normal&nbsp;<br />incidence.&nbsp; What order of&nbsp;dark fringes&nbsp;are observed at an angle <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.6.9.mode=Inline@
qu.6.9.name=Diffraction Grating - Find Angle - Bright ~ NG@
qu.6.9.comment=@
qu.6.9.editing=useHTML@
qu.6.9.solution=<p>For a diffraction grating, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.9.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$ans=arcsin(($m*$lambda*10^(-9))/($d*10^(-3)))*(360/(2*Pi));@
qu.6.9.uid=d777380a-3557-43a9-bc49-bd9189c01319@
qu.6.9.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.9.weighting=1@
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qu.6.9.part.1.numStyle= scientific  @
qu.6.9.part.1.editing=useHTML@
qu.6.9.part.1.showUnits=false@
qu.6.9.part.1.question=(Unset)@
qu.6.9.part.1.mode=Numeric@
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qu.6.9.part.1.negStyle=both@
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qu.6.9.part.1.answer.num=$ans@
qu.6.9.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>. If the<br />light&nbsp;incident on the slits is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what angle, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>degrees</mi></mrow></mstyle></math>, would one find&nbsp;<br />the&nbsp;order-$m bright fringes?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi></mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math></span></p>@

qu.6.10.mode=Inline@
qu.6.10.name=Single Slit Diffraction - Find Screen Height - Dark ~ NG@
qu.6.10.comment=@
qu.6.10.editing=useHTML@
qu.6.10.solution=<p>For a single slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Given the distance to the screen, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>y</mi><mrow><mi>$m</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$X</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>m</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.10.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$ans=tan(arcsin(($m*$lambda*10^(-9))/($d*10^(-3))))*$X*10^(2);@
qu.6.10.uid=365d4ffe-34bc-4716-bcf7-cf8a9d2b2fc2@
qu.6.10.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.10.weighting=1@
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qu.6.10.part.1.name=sro_id_1@
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qu.6.10.part.1.negStyle=both@
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qu.6.10.part.1.answer.num=$ans@
qu.6.10.question=<p>The slit in the diagram&nbsp;is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If the&nbsp;light&nbsp;incident&nbsp;on the slit is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>,<br />&nbsp;at what distance above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math> would&nbsp;one&nbsp;find&nbsp;the&nbsp;order-$m dark fringes on the screen, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="$X m" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math></span></p>@

qu.6.11.mode=Inline@
qu.6.11.name=Diffraction Grating - Find Distance to Screen - Bright ~ NG@
qu.6.11.comment=@
qu.6.11.editing=useHTML@
qu.6.11.solution=<p>For a diffraction grating, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Given <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>, we can then solve for:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>y</mi><mrow><mi>tan</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.11.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$y=rand(0.1,1.5,3);
$ans=($y*10^(-2))/tan(arcsin(($m*$lambda*10^(-9))/($d*10^(-3))));@
qu.6.11.uid=e06e0f20-c768-46a8-9ca3-1d0000c6e244@
qu.6.11.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.11.weighting=1@
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qu.6.11.part.1.name=sro_id_1@
qu.6.11.part.1.answer.units=@
qu.6.11.part.1.numStyle= scientific  @
qu.6.11.part.1.editing=useHTML@
qu.6.11.part.1.showUnits=false@
qu.6.11.part.1.question=(Unset)@
qu.6.11.part.1.mode=Numeric@
qu.6.11.part.1.grading=exact_sigd@
qu.6.11.part.1.negStyle=both@
qu.6.11.part.1.digit=3@
qu.6.11.part.1.answer.num=$ans@
qu.6.11.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If light&nbsp;incident&nbsp;on&nbsp;<br />the slits&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math> produces&nbsp;order-$m bright fringes&nbsp;on the screen <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>above&nbsp;<br />and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>, what is the distance <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi></mrow></mstyle></math>&nbsp;to the screen, in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math></span></p>@

qu.6.12.mode=Inline@
qu.6.12.name=Single Slit Diffraction - Find Wavelength - Dark ~ NG@
qu.6.12.comment=@
qu.6.12.editing=useHTML@
qu.6.12.solution=<p>For a single slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi></mrow></mfenced></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.12.algorithm=$d=rand(1.0,9.99,3);
$m=range(1,4);
$theta=rand(0,20,3);
$ans=($d*10^(-6))*sin($theta*2*Pi/360)*10^(9)/$m;@
qu.6.12.uid=fc9bd828-181f-4838-b090-7b929e89a3b0@
qu.6.12.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.12.weighting=1@
qu.6.12.numbering=alpha@
qu.6.12.part.1.name=sro_id_1@
qu.6.12.part.1.answer.units=@
qu.6.12.part.1.numStyle= scientific  @
qu.6.12.part.1.editing=useHTML@
qu.6.12.part.1.showUnits=false@
qu.6.12.part.1.question=(Unset)@
qu.6.12.part.1.mode=Numeric@
qu.6.12.part.1.grading=exact_sigd@
qu.6.12.part.1.negStyle=both@
qu.6.12.part.1.digit=3@
qu.6.12.part.1.answer.num=$ans@
qu.6.12.question=<p>The slit in the diagram&nbsp;is of width <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow><mrow></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of monochromatic light&nbsp;passes&nbsp;<br />through the slit at normal incidence.&nbsp; If the&nbsp;order-$m dark fringes are visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>, what is the&nbsp;<br />wavelength of the light, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math></span></p>@

qu.6.13.mode=Inline@
qu.6.13.name=Single Slit Diffraction - Find Distance to Screen - Dark ~ NG@
qu.6.13.comment=@
qu.6.13.editing=useHTML@
qu.6.13.solution=<p>For a single slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Given the height of the fringe on the screen, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mrow><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.13.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$y=rand(0.1,1.5,3);
$ans=($y*10^(-2))/tan(arcsin(($m*$lambda*10^(-9))/($d*10^(-3))));@
qu.6.13.uid=fcacf166-ffe0-4145-a789-3544d051fa43@
qu.6.13.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.6.13.part.1.answer.num=$ans@
qu.6.13.question=<p>The single slit in the diagram&nbsp;is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If&nbsp;light&nbsp;incident&nbsp;on&nbsp;the slit&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math><br />&nbsp;produces&nbsp;order-$m dark fringes&nbsp;on the screen&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>above&nbsp;and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>, what is the distance <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi></mrow></mstyle></math>&nbsp;to&nbsp;<br />the screen, in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math></span></p>@

qu.6.14.mode=Inline@
qu.6.14.name=Diffraction Grating - Find Wavelength - Bright ~ NG@
qu.6.14.comment=@
qu.6.14.editing=useHTML@
qu.6.14.solution=<p>For a diffraction grating, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow></mfenced><mrow><mi>$m</mi></mrow></mfrac><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.14.algorithm=$d=rand(1.0,9.99,3);
$m=range(1,4);
$theta=rand(0,20,3);
$ans=($d*10^(-6))*sin($theta*2*Pi/360)*10^(9)/$m;@
qu.6.14.uid=2ba15e3f-f277-4834-b6eb-2ff20a7350a7@
qu.6.14.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.14.weighting=1@
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qu.6.14.part.1.negStyle=both@
qu.6.14.part.1.digit=3@
qu.6.14.part.1.answer.num=$ans@
qu.6.14.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow><mrow></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A<br />beam of monochromatic light&nbsp;passes through the grating at normal incidence.&nbsp; If the&nbsp;order-$m bright&nbsp;<br />fringes are visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>, what is the wavelength of the light, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math></span></p>@

qu.6.15.mode=Inline@
qu.6.15.name=Single Slit Diffraction - Find Wavelength - Bright ~ NG@
qu.6.15.comment=@
qu.6.15.editing=useHTML@
qu.6.15.solution=<p>For a single slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mfenced><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.15.algorithm=$d=rand(1.0,9.99,3);
$m=range(1,4);
$theta=rand(0,20,3);
$ans=($d*10^(-6))*sin($theta*2*Pi/360)*10^(9)/($m/2);@
qu.6.15.uid=2297f795-49f4-46ae-904e-c72cf1d45572@
qu.6.15.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.15.weighting=1@
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qu.6.15.part.1.question=(Unset)@
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qu.6.15.part.1.negStyle=both@
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qu.6.15.part.1.answer.num=$ans@
qu.6.15.question=<p>The slit in the diagram&nbsp;is of&nbsp;width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow><mrow></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of monochromatic light&nbsp;passes&nbsp;<br />through the slit at normal incidence.&nbsp; If the&nbsp;order-$m bright fringes are visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>, what is the&nbsp;<br />wavelength of the light, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math></span></p>@

qu.6.16.mode=Inline@
qu.6.16.name=Single Slit Diffraction - Find Slit Spacing - Dark ~ NG@
qu.6.16.comment=@
qu.6.16.editing=useHTML@
qu.6.16.solution=<p>For a single slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.16.algorithm=$m=range(1,4);
$theta=rand(0,20,3);
$lambda=range(100,999);
$ans=$m*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360);@
qu.6.16.uid=4fd87028-0c14-49f1-9c6f-1a386695c318@
qu.6.16.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.6.16.question=<p>The&nbsp;slit in the diagram&nbsp;is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of&nbsp;monochromatic light&nbsp;passes through the&nbsp;<br />slit at normal incidence.&nbsp; If the&nbsp;order-$m dark fringes&nbsp;are&nbsp;visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;for light of wavelength&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>,&nbsp;what is the width of the slit <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math></span></p>@

qu.6.17.mode=Inline@
qu.6.17.name=Single Slit Diffraction - Find Slit Spacing - Bright ~ NG@
qu.6.17.comment=@
qu.6.17.editing=useHTML@
qu.6.17.solution=<p>For a single slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.17.algorithm=$m=range(1,4);
$theta=rand(0,20,3);
$lambda=range(100,999);
$ans=($m/2)*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360);@
qu.6.17.uid=79ffa25c-f1df-428e-8b73-e142b5311516@
qu.6.17.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.17.weighting=1@
qu.6.17.numbering=alpha@
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qu.6.17.part.1.answer.num=$ans@
qu.6.17.question=<p>The slit in the diagram&nbsp;is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of&nbsp;monochromatic light&nbsp;passes through the&nbsp;<br />slit at normal incidence.&nbsp; If the&nbsp;order-$m&nbsp;bright fringes&nbsp;are&nbsp;visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;for light of wavelength&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>,&nbsp;what is the slit width <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math></span></p>@

qu.6.18.mode=Inline@
qu.6.18.name=Single Slit Diffraction - Find Screen Height - Bright ~ NG@
qu.6.18.comment=@
qu.6.18.editing=useHTML@
qu.6.18.solution=<p>For a single slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;Given the distance to the screen, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>y</mi><mrow><mi>$m</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$X</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>m</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>@
qu.6.18.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$ans=tan(arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3))))*$X*10^(2);@
qu.6.18.uid=a661cb14-c98b-4ed0-a0b5-f1735f1bb74a@
qu.6.18.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.6.18.part.1.digit=3@
qu.6.18.part.1.answer.num=$ans@
qu.6.18.question=<p>The slit in the diagram&nbsp;is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If the&nbsp;light&nbsp;incident&nbsp;on the slit is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>,<br />&nbsp;at what distance above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math> would&nbsp;one&nbsp;find&nbsp;the&nbsp;order-$m bright fringes on the screen, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="$X m" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math></span></p>@

qu.6.19.mode=Inline@
qu.6.19.name=Diffraction Grating - Find Slit Spacing - Bright ~ NG@
qu.6.19.comment=@
qu.6.19.editing=useHTML@
qu.6.19.solution=<p>For a diffraction grating, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$</mi><mi>m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.19.algorithm=$m=range(1,4);
$theta=rand(0,20,3);
$lambda=range(100,999);
$ans=$m*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360);@
qu.6.19.uid=420174c0-e7df-4d7f-afb8-f267c2e56306@
qu.6.19.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.19.weighting=1@
qu.6.19.numbering=alpha@
qu.6.19.part.1.name=sro_id_1@
qu.6.19.part.1.answer.units=@
qu.6.19.part.1.numStyle= scientific  @
qu.6.19.part.1.editing=useHTML@
qu.6.19.part.1.showUnits=false@
qu.6.19.part.1.question=(Unset)@
qu.6.19.part.1.mode=Numeric@
qu.6.19.part.1.grading=exact_sigd@
qu.6.19.part.1.negStyle=both@
qu.6.19.part.1.digit=3@
qu.6.19.part.1.answer.num=$ans@
qu.6.19.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of&nbsp;<br />monochromatic light&nbsp;passes through the grating at normal incidence.&nbsp; If the&nbsp;order-$m bright&nbsp;fringes&nbsp;are&nbsp;<br />visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;for light of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>,&nbsp;what is the slit spacing <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math></span></p>@

qu.6.20.mode=Inline@
qu.6.20.name=Single Slit Diffraction - Find Fringe Order - Dark ~ NG@
qu.6.20.comment=@
qu.6.20.editing=useHTML@
qu.6.20.solution=<p>For a single slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow></mfrac><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.20.algorithm=$m=range(1,6);
$theta=rand(0,45,3);
$lambda=range(100,999);
$d=sig(3,$m*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360));@
qu.6.20.uid=373f7ac2-5bb2-4cd4-8698-e2ba16e02bc2@
qu.6.20.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.20.weighting=1@
qu.6.20.numbering=alpha@
qu.6.20.part.1.name=sro_id_1@
qu.6.20.part.1.answer.units=@
qu.6.20.part.1.numStyle= scientific  @
qu.6.20.part.1.editing=useHTML@
qu.6.20.part.1.showUnits=false@
qu.6.20.part.1.question=(Unset)@
qu.6.20.part.1.mode=Numeric@
qu.6.20.part.1.grading=exact_value@
qu.6.20.part.1.negStyle=both@
qu.6.20.part.1.answer.num=$m@
qu.6.20.question=<p>The slit in the diagram is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi></mrow><mrow><mi></mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mstyle></math>,&nbsp;with <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of&nbsp;monochromatic light&nbsp;of&nbsp;<br />wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>passes through the slit at normal&nbsp;incidence.&nbsp; What order of&nbsp;dark fringes&nbsp;are&nbsp;<br />observed at an angle <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.6.21.mode=Inline@
qu.6.21.name=Single Slit Diffraction - Find Distance to Screen - Bright ~ NG@
qu.6.21.comment=@
qu.6.21.editing=useHTML@
qu.6.21.solution=<p>For a single slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;Given the height of the fringe on the screen, we can find the distance to the screen:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mrow><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.6.21.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$y=rand(0.1,1.5,3);
$ans=($y*10^(-2))/tan(arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3))));@
qu.6.21.uid=fce233ad-625a-45f9-a410-30a3bf747cc6@
qu.6.21.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.21.weighting=1@
qu.6.21.numbering=alpha@
qu.6.21.part.1.name=sro_id_1@
qu.6.21.part.1.answer.units=@
qu.6.21.part.1.numStyle= scientific  @
qu.6.21.part.1.editing=useHTML@
qu.6.21.part.1.showUnits=false@
qu.6.21.part.1.question=(Unset)@
qu.6.21.part.1.mode=Numeric@
qu.6.21.part.1.grading=exact_sigd@
qu.6.21.part.1.negStyle=both@
qu.6.21.part.1.digit=3@
qu.6.21.part.1.answer.num=$ans@
qu.6.21.question=<p>The slit in the diagram is of width&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If&nbsp;light&nbsp;incident&nbsp;on&nbsp;the slit&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>&nbsp;<br />produces&nbsp;order-$m bright fringes&nbsp;on the screen&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>above&nbsp;and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>, what is the distance <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi></mrow></mstyle></math>&nbsp;to&nbsp;<br />the screen, in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramSingleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math></span></p>@

qu.6.22.mode=Inline@
qu.6.22.name=Diffraction Grating - Find Angle - Dark ~ NG@
qu.6.22.comment=@
qu.6.22.editing=useHTML@
qu.6.22.solution=<p>For a diffraction grating, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.22.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$ans=arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3)))*(360/(2*Pi));@
qu.6.22.uid=9a753850-0b3b-4072-a9d5-126013345e44@
qu.6.22.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.22.weighting=1@
qu.6.22.numbering=alpha@
qu.6.22.part.1.name=sro_id_1@
qu.6.22.part.1.answer.units=@
qu.6.22.part.1.numStyle= scientific  @
qu.6.22.part.1.editing=useHTML@
qu.6.22.part.1.showUnits=false@
qu.6.22.part.1.question=(Unset)@
qu.6.22.part.1.mode=Numeric@
qu.6.22.part.1.grading=exact_sigd@
qu.6.22.part.1.negStyle=both@
qu.6.22.part.1.digit=3@
qu.6.22.part.1.answer.num=$ans@
qu.6.22.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>. If the<br />light&nbsp;incident on the slits is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what angle, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>degrees</mi></mrow></mstyle></math>, would one find&nbsp;<br />the&nbsp;order-$m dark fringes?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mrow></mrow><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math></span></p>@

qu.6.23.mode=Inline@
qu.6.23.name=Diffraction Grating - Find Wavelength - Dark ~ NG@
qu.6.23.comment=@
qu.6.23.editing=useHTML@
qu.6.23.solution=<p>For a diffraction grating, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow></mfenced><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.23.algorithm=$d=rand(1.0,9.99,3);
$m=range(1,4);
$theta=rand(0,20,3);
$ans=($d*10^(-6))*sin($theta*2*Pi/360)*10^(9)/($m/2);@
qu.6.23.uid=0e01a92b-69e9-417e-b66e-241f481daa07@
qu.6.23.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.23.weighting=1@
qu.6.23.numbering=alpha@
qu.6.23.part.1.name=sro_id_1@
qu.6.23.part.1.answer.units=@
qu.6.23.part.1.numStyle= scientific  @
qu.6.23.part.1.editing=useHTML@
qu.6.23.part.1.showUnits=false@
qu.6.23.part.1.question=(Unset)@
qu.6.23.part.1.mode=Numeric@
qu.6.23.part.1.grading=exact_sigd@
qu.6.23.part.1.negStyle=both@
qu.6.23.part.1.digit=3@
qu.6.23.part.1.answer.num=$ans@
qu.6.23.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow><mrow></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A<br />beam of monochromatic light&nbsp;passes through the grating at normal incidence.&nbsp; If the&nbsp;order-$m dark<br />fringes are visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>, what is the wavelength of the light, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math></span></p>@

qu.6.24.mode=Inline@
qu.6.24.name=Diffraction Grating - Find Distance to Screen - Dark ~ NG@
qu.6.24.comment=@
qu.6.24.editing=useHTML@
qu.6.24.solution=<p>For a diffraction grating, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Given that the fringes occur at a height <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mrow><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.6.24.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$y=rand(0.1,1.5,3);
$ans=($y*10^(-2))/tan(arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3))));@
qu.6.24.uid=a9740f61-d2f5-4b76-9535-5f900cd2baad@
qu.6.24.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Diffraction;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.6.24.weighting=1@
qu.6.24.numbering=alpha@
qu.6.24.part.1.name=sro_id_1@
qu.6.24.part.1.answer.units=@
qu.6.24.part.1.numStyle= scientific  @
qu.6.24.part.1.editing=useHTML@
qu.6.24.part.1.showUnits=false@
qu.6.24.part.1.question=(Unset)@
qu.6.24.part.1.mode=Numeric@
qu.6.24.part.1.grading=exact_sigd@
qu.6.24.part.1.negStyle=both@
qu.6.24.part.1.digit=3@
qu.6.24.part.1.answer.num=$ans@
qu.6.24.question=<p>The narrow slits of a diffraction grating are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If light&nbsp;incident&nbsp;on&nbsp;<br />the slits&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math> produces&nbsp;order-$m dark fringes&nbsp;on the screen <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>above&nbsp;<br />and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>, what is the distance <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi></mrow></mstyle></math>&nbsp;to the screen, in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramGrating.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math></span></p>@

qu.7.topic=EM Waves@

qu.7.1.mode=Inline@
qu.7.1.name=Electromagnetic Wave Amplitude - B to E ~ NG@
qu.7.1.comment=@
qu.7.1.editing=useHTML@
qu.7.1.solution=<p>For electromagnetic radiation, the magnitudes of the amplitudes of the fields are related by:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>E</mi><mrow><mi>B</mi></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>c</mi></mrow></mstyle></math>.</p>@
qu.7.1.algorithm=$B=rand(1.00,9.99,3);
$Bex=range(5,10);
$ans=(3.00*10^(8))*$B*10^($Bex);@
qu.7.1.uid=97f34f83-6542-4630-9c7e-69bbd43ecdcf@
qu.7.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Electromagnetic Wave Magnitude;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.7.1.weighting=1@
qu.7.1.numbering=alpha@
qu.7.1.part.1.name=sro_id_1@
qu.7.1.part.1.answer.units=@
qu.7.1.part.1.numStyle= scientific  @
qu.7.1.part.1.editing=useHTML@
qu.7.1.part.1.showUnits=false@
qu.7.1.part.1.question=(Unset)@
qu.7.1.part.1.mode=Numeric@
qu.7.1.part.1.grading=exact_sigd@
qu.7.1.part.1.negStyle=both@
qu.7.1.part.1.digit=3@
qu.7.1.part.1.answer.num=$ans@
qu.7.1.question=<p>A particular electromagnetic wave has a maximum magnetic field amplitude of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$B</mi></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Bex</mi></mrow></msup><mi>T</mi></mrow></mstyle></math>, what is&nbsp;<br />the maximum electric field amplitude, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math></span></p>@

qu.7.2.mode=Inline@
qu.7.2.name=Electromagnetic Wave Amplitude - E to B ~ NG@
qu.7.2.comment=@
qu.7.2.editing=useHTML@
qu.7.2.solution=<p>For electromagnetic radiation, the magnitudes of the amplitudes of the fields are related by:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>E</mi><mrow><mi>B</mi></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>c</mi></mrow></mstyle></math>.</p>@
qu.7.2.algorithm=$E=rand(1.00,9.99,3);
$Eex=range(12,16);
$ans=($E*10^($Eex))/(3.00*10^(8));@
qu.7.2.uid=4faab6a8-f12d-4ea2-892c-d65794e376e5@
qu.7.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Electromagnetic Wave Magnitude;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.7.2.weighting=1@
qu.7.2.numbering=alpha@
qu.7.2.part.1.name=sro_id_1@
qu.7.2.part.1.answer.units=@
qu.7.2.part.1.numStyle= scientific  @
qu.7.2.part.1.editing=useHTML@
qu.7.2.part.1.showUnits=false@
qu.7.2.part.1.question=(Unset)@
qu.7.2.part.1.mode=Numeric@
qu.7.2.part.1.grading=exact_sigd@
qu.7.2.part.1.negStyle=both@
qu.7.2.part.1.digit=3@
qu.7.2.part.1.answer.num=$ans@
qu.7.2.question=<p>A particular electromagnetic wave has a maximum electric field amplitude of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$E</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$Eex</mi></mrow></msup><mfrac><mi>V</mi><mrow><mi>m</mi></mrow></mfrac></mrow></mstyle></math>, what is&nbsp;<br />the maximum magnetic field amplitude, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>T</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>T</mi></mrow></mstyle></math></span></p>@

qu.8.topic=Interference@

qu.8.1.mode=Inline@
qu.8.1.name=Double Slit Interference - Find Screen Height - Bright ~ NG@
qu.8.1.comment=@
qu.8.1.editing=useHTML@
qu.8.1.solution=<p>For a double slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;Given the distance to the screen, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$X</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>m</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>@
qu.8.1.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$ans=tan(arcsin(($m*$lambda*10^(-9))/($d*10^(-3))))*$X*10^(2);@
qu.8.1.uid=a845e0a3-54ff-490e-afe5-bd2ee5ce0fa5@
qu.8.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.8.1.weighting=1@
qu.8.1.numbering=alpha@
qu.8.1.part.1.name=sro_id_1@
qu.8.1.part.1.answer.units=@
qu.8.1.part.1.numStyle= scientific  @
qu.8.1.part.1.editing=useHTML@
qu.8.1.part.1.showUnits=false@
qu.8.1.part.1.question=(Unset)@
qu.8.1.part.1.mode=Numeric@
qu.8.1.part.1.grading=exact_sigd@
qu.8.1.part.1.negStyle=both@
qu.8.1.part.1.digit=3@
qu.8.1.part.1.answer.num=$ans@
qu.8.1.question=<p>The centres of the two slits in the diagram are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If the&nbsp;coherent<br />light&nbsp;incident&nbsp;on the slits is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what distance above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math> would&nbsp;<br />one&nbsp;find&nbsp;the&nbsp;order-$m bright fringes on the screen, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="$X m" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math></span></p>@

qu.8.2.mode=Inline@
qu.8.2.name=Double Slit Interference - Find Wavelength - Dark ~ NG@
qu.8.2.comment=@
qu.8.2.editing=useHTML@
qu.8.2.solution=<p>For a double slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn mathvariant='italic'>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced></mrow></mfrac><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.2.algorithm=$d=rand(1.0,9.99,3);
$m=range(1,4);
$theta=rand(0,20,3);
$ans=($d*10^(-6))*sin($theta*2*Pi/360)*10^(9)/($m/2);@
qu.8.2.uid=0e728ed5-18b9-4ac3-af45-482b8d152289@
qu.8.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.8.2.weighting=1@
qu.8.2.numbering=alpha@
qu.8.2.part.1.name=sro_id_1@
qu.8.2.part.1.answer.units=@
qu.8.2.part.1.numStyle= scientific  @
qu.8.2.part.1.editing=useHTML@
qu.8.2.part.1.showUnits=false@
qu.8.2.part.1.question=(Unset)@
qu.8.2.part.1.mode=Numeric@
qu.8.2.part.1.grading=exact_sigd@
qu.8.2.part.1.negStyle=both@
qu.8.2.part.1.digit=3@
qu.8.2.part.1.answer.num=$ans@
qu.8.2.question=<p>The centres of the two slits in the diagram&nbsp;are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow><mrow></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A<br />beam of monochromatic, coherent&nbsp;light&nbsp;passes through the slits at normal incidence.&nbsp; If the&nbsp;order-$m&nbsp;<br />dark fringes are visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>, what is the wavelength of the light, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math></span></p>@

qu.8.3.mode=Inline@
qu.8.3.name=Double Slit Interference - Find Fringe Order - Bright ~ NG@
qu.8.3.comment=@
qu.8.3.editing=useHTML@
qu.8.3.solution=<p>For a double slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.3.algorithm=$m=range(1,6);
$theta=rand(0,45,3);
$lambda=range(100,999);
$d=sig(3,$m*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360));@
qu.8.3.uid=4a605214-ddcc-4c36-9044-45e4db556c81@
qu.8.3.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.8.3.weighting=1@
qu.8.3.numbering=alpha@
qu.8.3.part.1.name=sro_id_1@
qu.8.3.part.1.answer.units=@
qu.8.3.part.1.numStyle= scientific  @
qu.8.3.part.1.editing=useHTML@
qu.8.3.part.1.showUnits=false@
qu.8.3.part.1.question=(Unset)@
qu.8.3.part.1.mode=Numeric@
qu.8.3.part.1.grading=exact_value@
qu.8.3.part.1.negStyle=both@
qu.8.3.part.1.answer.num=$m@
qu.8.3.question=<p>The centres of the two slits in the diagram&nbsp;are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi></mrow><mrow><mi></mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mstyle></math>,&nbsp;with <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A&nbsp;<br />beam of&nbsp;monochromatic, coherent light&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>passes through the slits at normal&nbsp;<br />incidence.&nbsp; What order of&nbsp;bright fringes&nbsp;are observed at an angle <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.8.4.mode=Inline@
qu.8.4.name=Double Slit Interference - Find Slit Spacing - Dark ~ NG@
qu.8.4.comment=@
qu.8.4.editing=useHTML@
qu.8.4.solution=<p>For a double slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn mathvariant='italic'>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.4.algorithm=$m=range(1,4);
$theta=rand(0,20,3);
$lambda=range(100,999);
$ans=($m/2)*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360);@
qu.8.4.uid=fb993b35-fcde-4e71-a1b2-c4370572df83@
qu.8.4.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.8.4.weighting=1@
qu.8.4.numbering=alpha@
qu.8.4.part.1.name=sro_id_1@
qu.8.4.part.1.answer.units=@
qu.8.4.part.1.numStyle= scientific  @
qu.8.4.part.1.editing=useHTML@
qu.8.4.part.1.showUnits=false@
qu.8.4.part.1.question=(Unset)@
qu.8.4.part.1.mode=Numeric@
qu.8.4.part.1.grading=exact_sigd@
qu.8.4.part.1.negStyle=both@
qu.8.4.part.1.digit=3@
qu.8.4.part.1.answer.num=$ans@
qu.8.4.question=<p>The centres of the two slits in the diagram&nbsp;are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of&nbsp;<br />monochromatic, coherent&nbsp;light&nbsp;passes through the slits at normal incidence.&nbsp; If the&nbsp;order-$m dark&nbsp;<br />fringes&nbsp;are&nbsp;visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;for light of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>,&nbsp;what is the slit spacing <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math></span></p>@

qu.8.5.mode=Inline@
qu.8.5.name=Double Slit Interference - Find Angle - Bright ~ NG@
qu.8.5.comment=@
qu.8.5.editing=useHTML@
qu.8.5.solution=<p>For a double slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.5.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$ans=arcsin(($m*$lambda*10^(-9))/($d*10^(-3)))*(360/(2*Pi));@
qu.8.5.uid=10fdce46-567b-4573-852b-62d3b343ca31@
qu.8.5.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.8.5.weighting=1@
qu.8.5.numbering=alpha@
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qu.8.5.part.1.negStyle=both@
qu.8.5.part.1.digit=3@
qu.8.5.part.1.answer.num=$ans@
qu.8.5.question=<p>The centres of the two slits in the diagram are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>. If&nbsp;<br />the coherent&nbsp;light&nbsp;incident on the slits is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what angle, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>degrees</mi></mrow></mstyle></math>,&nbsp;<br />would one find&nbsp;the&nbsp;order-$m bright fringes?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi></mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math></span></p>@

qu.8.6.mode=Inline@
qu.8.6.name=Double Slit Interference - Find Screen Height - Dark ~ NG@
qu.8.6.comment=@
qu.8.6.editing=useHTML@
qu.8.6.solution=<p>For a double slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn mathvariant='italic'>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;Given the distance to the screen, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$X</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>m</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>@
qu.8.6.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$ans=tan(arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3))))*$X*10^(2);@
qu.8.6.uid=68146528-4628-433e-9501-9d1d213ca5d3@
qu.8.6.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.8.6.part.1.showUnits=false@
qu.8.6.part.1.question=(Unset)@
qu.8.6.part.1.mode=Numeric@
qu.8.6.part.1.grading=exact_sigd@
qu.8.6.part.1.negStyle=both@
qu.8.6.part.1.digit=3@
qu.8.6.part.1.answer.num=$ans@
qu.8.6.question=<p>The centres of the two slits in the diagram are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If the&nbsp;coherent<br />light&nbsp;incident&nbsp;on the slits is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what distance above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math> would&nbsp;<br />one&nbsp;find&nbsp;the&nbsp;order-$m dark fringes on the screen, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="$X m" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>cm</mi></mrow></mstyle></math></span></p>@

qu.8.7.mode=Inline@
qu.8.7.name=Double Slit Interference - Find Slit Spacing - Bright ~ NG@
qu.8.7.comment=@
qu.8.7.editing=useHTML@
qu.8.7.solution=<p>For a double slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.7.algorithm=$m=range(1,4);
$theta=rand(0,20,3);
$lambda=range(100,999);
$ans=$m*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360);@
qu.8.7.uid=c2f5d4c0-906a-4765-802e-32398d45eaae@
qu.8.7.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.8.7.weighting=1@
qu.8.7.numbering=alpha@
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qu.8.7.part.1.editing=useHTML@
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qu.8.7.part.1.question=(Unset)@
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qu.8.7.part.1.negStyle=both@
qu.8.7.part.1.digit=3@
qu.8.7.part.1.answer.num=$ans@
qu.8.7.question=<p>The centres of the two slits in the diagram&nbsp;are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A beam of&nbsp;<br />monochromatic, coherent&nbsp;light&nbsp;passes through the slits at normal incidence.&nbsp; If the&nbsp;order-$m&nbsp;<br />bright&nbsp;fringes&nbsp;are&nbsp;visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;for light of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>,&nbsp;what is the slit spacing <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow></mstyle></math>, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;m</mi></mrow></mstyle></math></span></p>@

qu.8.8.mode=Inline@
qu.8.8.name=Double Slit Interference - Find Fringe Order - Dark ~ NG@
qu.8.8.comment=@
qu.8.8.editing=useHTML@
qu.8.8.solution=<p>For a double slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn mathvariant='italic'>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow></mfrac><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.8.algorithm=$m=range(1,6);
$theta=rand(0,45,3);
$lambda=range(100,999);
$d=sig(3,($m/2)*$lambda*10^(-9)*10^(6)/sin($theta*2*Pi/360));@
qu.8.8.uid=e32d2ffd-a9af-42b4-94f5-e906c1251799@
qu.8.8.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.8.8.part.1.grading=exact_value@
qu.8.8.part.1.negStyle=both@
qu.8.8.part.1.answer.num=$m@
qu.8.8.question=<p>The centres of the two slits in the diagram&nbsp;are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi></mrow><mrow><mi></mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mstyle></math>,&nbsp;with <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A&nbsp;<br />beam of&nbsp;monochromatic, coherent&nbsp;light&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>passes through the slits at normal&nbsp;<br />incidence.&nbsp; What order of&nbsp;dark fringes&nbsp;are observed at an angle <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>&nbsp;above and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.8.9.mode=Inline@
qu.8.9.name=Double Slit Interference - Find Wavelength - Bright ~ NG@
qu.8.9.comment=@
qu.8.9.editing=useHTML@
qu.8.9.solution=<p>For a double slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&mu;m</mi></mrow></mfenced><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi></mrow></mfenced></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.9.algorithm=$d=rand(1.0,9.99,3);
$m=range(1,4);
$theta=rand(0,20,3);
$ans=($d*10^(-6))*sin($theta*2*Pi/360)*10^(9)/$m;@
qu.8.9.uid=f5999010-2bb7-456c-8e8c-75d5d4b7a6c2@
qu.8.9.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.8.9.weighting=1@
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qu.8.9.part.1.answer.units=@
qu.8.9.part.1.numStyle= scientific  @
qu.8.9.part.1.editing=useHTML@
qu.8.9.part.1.showUnits=false@
qu.8.9.part.1.question=(Unset)@
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qu.8.9.part.1.negStyle=both@
qu.8.9.part.1.digit=3@
qu.8.9.part.1.answer.num=$ans@
qu.8.9.question=<p>The centres of the two slits in the diagram&nbsp;are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>&mu;</mi></mrow><mi>m</mi></mrow><mrow></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>.&nbsp; A<br />beam of monochromatic, coherent&nbsp;light&nbsp;passes through the slits at normal incidence.&nbsp; If the&nbsp;order-$m&nbsp;<br />bright&nbsp;fringes are visible at <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>$theta</mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math>, what is the wavelength of the light, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>nm</mi></mrow></mstyle></math></span></p>@

qu.8.10.mode=Inline@
qu.8.10.name=Double Slit Interference - Find Distance to Screen - Bright ~ NG@
qu.8.10.comment=@
qu.8.10.editing=useHTML@
qu.8.10.solution=<p>For a double slit, constructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mi>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>Given the height of the fringes, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mrow><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.10.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$y=rand(0.1,1.5,3);
$ans=($y*10^(-2))/tan(arcsin(($m*$lambda*10^(-9))/($d*10^(-3))));@
qu.8.10.uid=45cea83b-50d5-4bea-9f27-24b07b701001@
qu.8.10.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
@
qu.8.10.weighting=1@
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qu.8.10.part.1.name=sro_id_1@
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qu.8.10.part.1.question=(Unset)@
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qu.8.10.question=<p>The centres of the two slits in the diagram are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If coherent&nbsp;<br />light&nbsp;incident&nbsp;on&nbsp;the slits&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math> produces&nbsp;order-$m bright fringes&nbsp;on the screen&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>above&nbsp;and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>, what is the distance <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi></mrow></mstyle></math>&nbsp;to the screen, in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math></span></p>@

qu.8.11.mode=Inline@
qu.8.11.name=Double Slit Interference - Find Distance to Screen - Dark ~ NG@
qu.8.11.comment=@
qu.8.11.editing=useHTML@
qu.8.11.solution=<p>For a double slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn mathvariant='italic'>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;Given the fringe height, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mfenced><mrow><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.8.11.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$X=rand(1.00,9.00,3);
$y=rand(0.1,1.5,3);
$ans=($y*10^(-2))/tan(arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3))));@
qu.8.11.uid=04de4954-66df-4f9a-bd24-307d1a5e9060@
qu.8.11.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
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qu.8.11.question=<p>The centres of the two slits in the diagram are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>.&nbsp; If&nbsp;coherent<br />light&nbsp;incident&nbsp;on&nbsp;the slits&nbsp;of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math> produces&nbsp;order-$m dark fringes&nbsp;on the screen&nbsp;<br /><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>cm</mi></mrow></mstyle></math>above&nbsp;and below <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>P</mi></mrow></mstyle></math>, what is the distance <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi></mrow></mstyle></math>&nbsp;to the screen, in&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math>?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>m</mi></mrow></mstyle></math></span></p>@

qu.8.12.mode=Inline@
qu.8.12.name=Double Slit Interference - Find Angle - Dark ~ NG@
qu.8.12.comment=@
qu.8.12.editing=useHTML@
qu.8.12.solution=<p>For a double slit, destructive interference occurs when the parameters satisfy:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn mathvariant='italic'>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&lambda;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>d</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>.</p>
<p>Thus, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&theta;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msup><mi>sin</mi><mn>-1</mn></msup><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$m</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mfenced></mrow><mrow><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.8.12.algorithm=$d=rand(0.5,0.9,3);
$m=range(1,4);
$lambda=range(400,800);
$ans=arcsin((($m/2)*$lambda*10^(-9))/($d*10^(-3)))*(360/(2*Pi));@
qu.8.12.uid=919fb2c7-836d-4efa-80ba-2fabc0e1f355@
qu.8.12.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Two Source Interference;
  Difficulty=Medium;
  Features=Algorithmic;
  Features=Diagram;
@
qu.8.12.weighting=1@
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qu.8.12.part.1.digit=3@
qu.8.12.part.1.answer.num=$ans@
qu.8.12.question=<p>The centres of the two slits in the diagram are&nbsp;separated by a distance of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>d</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$d</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow><mrow><mi></mi></mrow></mstyle></math>, and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>X</mi><mrow><mo lspace='0.0em' rspace='0.0em'>&Gt;</mo></mrow><mi>d</mi></mrow></mstyle></math>. If&nbsp;<br />the coherent light&nbsp;incident on the slits is of wavelength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$lambda</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>nm</mi></mrow></mstyle></math>, at what angle, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>degrees</mi></mrow></mstyle></math>,&nbsp;<br />would one find&nbsp;the&nbsp;order-$m dark fringes?</p><p>&nbsp;</p><p><applet archive="modules/applets.jar" code="applets.labelImage.LabelImage" width="593" height="500"><param name="image" value="__BASE_URI__img/Interference/DiagramDoubleSlit.png" /><param name="size" value="1" /><param name="label.1.x" value="230" /><param name="label.1.y" value="10" /><param name="label.1.text" value="X" /></applet></p><p>&nbsp;</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi></mi><mrow><mi>o</mi></mrow></msup></mrow></mstyle></math></span></p>@

qu.9.topic=Potential Energy@

qu.9.1.mode=Inline@
qu.9.1.name=Electrical Potential Energy - Conservation - Find Charge ~ NG@
qu.9.1.comment=@
qu.9.1.editing=useHTML@
qu.9.1.solution=<p>Since the Coulomb force changes based on separation, it is easiest to use conservation of energy instead of forces to solve this problem.</p>
<p>&nbsp;Assuming that the moving particle starts at infinity, it will have no electric potential energy between it and the stationary particle.&nbsp; Thus, initially we only have the kinetic energy of the moving particle.&nbsp; At the point of closest approach, the initially moving particle will temporarily have zero kinetic energy - there will only be electric potential energy.&nbsp; As a result, the conservation equation is:</p>
<p>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac><msub><mi>m</mi><mrow><mn>1</mn></mrow></msub><msubsup><mi>v</mi><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msub><mi>kq</mi><mrow><mn>1</mn></mrow></msub><msub><mi>q</mi><mrow><mn>2</mn></mrow></msub></mrow><mrow><msup><mi>r</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Solving for the charge of the moving particle, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>q</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$m1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$m1ex</mi></mrow></msup><mi>kg</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><mi>k</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$q2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q2ex</mi></mrow></msup><mi>C</mi></mrow></mfenced></mrow></mfrac></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.9.1.algorithm=$m1=rand(1.0,9.99,3);
$m1ex=range(19,25);
$v=rand(1.0,9.99,3);
$vex=range(4,7);
$idx=range(0,1);
$q2=switch($idx,rand(1.0,9.99,3),-rand(1.0,9.99,3));
$q2ex=range(10,15);
$r=rand(1.0,9.99,3);
$ans=($r*10^(-3))*($m1*10^(-$m1ex))*(($v*10^($vex))^2)/(2*($q2*10^(-$q2ex))*(8.98755*10^(9)));@
qu.9.1.uid=e1790fe2-eb2c-415f-b843-8c4240d75707@
qu.9.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Electrical Potential Energy;
  Difficulty=Medium;
  Features=Algorithmic;
@
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qu.9.1.part.1.digit=3@
qu.9.1.part.1.answer.num=$ans@
qu.9.1.question=<p>A charged particle of mass&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$m1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$m1ex</mi></mrow></msup><mi>kg</mi></mrow></mstyle></math> is travelling at&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math> towards a second<br />charged particle that is fixed in space. The fixed particle has a charge of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$q2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q2ex</mi></mrow></msup><mi>C</mi></mrow></mstyle></math>.&nbsp; What&nbsp;<br />charge, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>,&nbsp;must the travelling particle have if it comes to a stop <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mstyle></math> before it collides with the fixed particle?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math></span></p>@

qu.9.2.mode=Inline@
qu.9.2.name=Electrical Potential Energy - Conservation - Find Speed ~ NG@
qu.9.2.comment=@
qu.9.2.editing=useHTML@
qu.9.2.solution=<p>Since the Coulomb force changes based on separation, it is easiest to use conservation of energy instead of forces to solve this problem.</p>
<p>&nbsp;Assuming that the moving particle starts at infinity, it will have no electric potential energy between it and the stationary particle.&nbsp; Thus, initially we only have the kinetic energy of the moving particle.&nbsp; At the point of closest approach, the initially moving particle will temporarily have zero kinetic energy - there will only be electric potential energy.&nbsp; As a result, the conservation equation is:</p>
<p>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac><msub><mi>m</mi><mrow><mn>1</mn></mrow></msub><msubsup><mi>v</mi><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msub><mi>kq</mi><mrow><mn>1</mn></mrow></msub><msub><mi>q</mi><mrow><mn>2</mn></mrow></msub></mrow><mrow><msup><mi>r</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Solving for the initial speed of the particle, we have:<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>v</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow><mrow><msqrt><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>k</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$q1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q1ex</mi></mrow></msup><mi>C</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$q2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q2ex</mi></mrow></msup><mi>C</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$m1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$m1ex</mi></mrow></msup><mi>kg</mi></mrow></mfenced></mrow></mfrac></mrow></mfenced></mrow></msqrt></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.9.2.algorithm=$m1=rand(1.0,9.99,3);
$m1ex=range(19,25);
$idx=range(0,1);
$q1=switch($idx,rand(1.0,9.99,3),-rand(1.0,9.99,3));
$q1ex=range(10,15);
$q2=switch($idx,rand(1.0,9.99,3),-rand(1.0,9.99,3));
$q2ex=range(10,15);
$r=rand(1.0,9.99,3);
$ans=sqrt((2*($q2*10^(-$q2ex))*(8.98755*10^(9))*($q1*10^(-$q1ex)))/(($r*10^(-3))*($m1*10^(-$m1ex))));@
qu.9.2.uid=623de630-cbc8-4daa-ab0a-bddf7a60dc01@
qu.9.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Electrical Potential Energy;
  Difficulty=Medium;
  Features=Algorithmic;
@
qu.9.2.weighting=1@
qu.9.2.numbering=alpha@
qu.9.2.part.1.name=sro_id_1@
qu.9.2.part.1.answer.units=@
qu.9.2.part.1.numStyle= scientific  @
qu.9.2.part.1.editing=useHTML@
qu.9.2.part.1.showUnits=false@
qu.9.2.part.1.question=(Unset)@
qu.9.2.part.1.mode=Numeric@
qu.9.2.part.1.grading=exact_sigd@
qu.9.2.part.1.negStyle=both@
qu.9.2.part.1.digit=3@
qu.9.2.part.1.answer.num=$ans@
qu.9.2.question=<p>A charged particle of mass&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$m1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$m1ex</mi></mrow></msup><mi>kg</mi></mrow></mstyle></math> is travelling from infinity&nbsp;towards a second&nbsp;<br />charged particle that is fixed in space. The moving particle has a charge of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$q2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q2ex</mi></mrow></msup><mi>C</mi></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow><mrow></mrow></mstyle></math>, while&nbsp;<br />the fixed particle has&nbsp;a charge of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$q1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q1ex</mi></mrow></msup><mi>C</mi></mrow></mstyle></math>.&nbsp;&nbsp;If the particles come within&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mstyle></math> of&nbsp;<br />eachother, what was the initial speed of the travelling particle, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math>?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math></span></p>@

qu.9.3.mode=Inline@
qu.9.3.name=Electrical Potential Energy - Conservation - Find Charge 2 ~ NG@
qu.9.3.comment=@
qu.9.3.editing=useHTML@
qu.9.3.solution=<p>Since the Coulomb force changes based on separation, it is easiest to use conservation of energy instead of forces to solve this problem.</p>
<p>&nbsp;Assuming that the moving particle starts at infinity, it will have no electric potential energy between it and the stationary particle.&nbsp; Thus, initially we only have the kinetic energy of the moving particle.&nbsp; At the point of closest approach, the initially moving particle will temporarily have zero kinetic energy - there will only be electric potential energy.&nbsp; As a result, the conservation equation is:</p>
<p>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac><msub><mi>m</mi><mrow><mn>1</mn></mrow></msub><msubsup><mi>v</mi><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msub><mi>kq</mi><mrow><mn>1</mn></mrow></msub><msub><mi>q</mi><mrow><mn>2</mn></mrow></msub></mrow><mrow><msup><mi>r</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mstyle></math>.</p>
<p>Solving for the charge of the stationary particle, we have:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>q</mi><mrow><mn>2</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac><mfenced open='(' close=')' separators=','><mrow><mi>$m1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$m1ex</mi></mrow></msup><mi>kg</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mi>s</mi></mrow></mfrac></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><mi>k</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$q2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q2ex</mi></mrow></msup><mi>C</mi></mrow></mfenced></mrow></mfrac></mrow></mfenced></mrow></mstyle></math>.</p>
<p>&nbsp;</p>@
qu.9.3.algorithm=$m1=rand(1.0,9.99,3);
$m1ex=range(19,25);
$v=rand(1.0,9.99,3);
$vex=range(4,7);
$idx=range(0,1);
$q2=switch($idx,rand(1.0,9.99,3),-rand(1.0,9.99,3));
$q2ex=range(10,15);
$r=rand(1.0,9.99,3);
$ans=($r*10^(-3))*($m1*10^(-$m1ex))*(($v*10^($vex))^2)/(2*($q2*10^(-$q2ex))*(8.98755*10^(9)));@
qu.9.3.uid=d935ec61-72ee-430d-8fdb-ed96b31588d8@
qu.9.3.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Electrical Potential Energy;
  Difficulty=Medium;
  Features=Algorithmic;
@
qu.9.3.weighting=1@
qu.9.3.numbering=alpha@
qu.9.3.part.1.name=sro_id_1@
qu.9.3.part.1.answer.units=@
qu.9.3.part.1.numStyle= scientific  @
qu.9.3.part.1.editing=useHTML@
qu.9.3.part.1.showUnits=false@
qu.9.3.part.1.question=(Unset)@
qu.9.3.part.1.mode=Numeric@
qu.9.3.part.1.grading=exact_sigd@
qu.9.3.part.1.negStyle=both@
qu.9.3.part.1.digit=3@
qu.9.3.part.1.answer.num=$ans@
qu.9.3.question=<p>A charged particle of mass&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$m1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$m1ex</mi></mrow></msup><mi>kg</mi></mrow></mstyle></math> is travelling at&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$v</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mi>$vex</mi></mrow></msup><mfrac><mi>m</mi><mrow><mi>s</mi></mrow></mfrac></mrow></mstyle></math> towards a second&nbsp;<br />charged particle that is fixed in space. The moving particle has a charge of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$q2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$q2ex</mi></mrow></msup><mi>C</mi></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow><mrow></mrow></mstyle></math>.&nbsp;<br />&nbsp;What charge, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math>,&nbsp;must the fixed particle have if the particles come within&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$r</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mstyle></math> of eachother?</p><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>C</mi></mrow></mstyle></math></span></p>@

qu.10.topic=Resistance@

qu.10.1.mode=Inline@
qu.10.1.name=Resistivity - Find Resistivity ~ NG@
qu.10.1.comment=@
qu.10.1.editing=useHTML@
qu.10.1.solution=<p>Resistance is related to resistivity by:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>&rho;L</mi><mrow><mi>A</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given the&nbsp;potential difference and current thus we can&nbsp;replace the resistance using&nbsp;Ohm's Law</p>
<p>So,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&rho;</mi></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>V</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>A</mi></mrow><mrow><mi>I</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>L</mi></mrow></mfrac></mrow><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mi>&rho;</mi></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Vex</mi></mrow></msup><mi>V</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$A</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msup><mi>mm</mi><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.10.1.algorithm=$L=rand(1.00,9.99,3);
$V=rand(1.00,9.99,3);
$Vex=range(1,5);
$I=rand(1.00,9.99,3);
$A=rand(0.100,0.999,3);
$ans=($A*10^(-6))*($V*10^(-$Vex))/(($L*10^(-3))*$I);@
qu.10.1.uid=4582a349-3cb5-4760-8963-f8dc152da078@
qu.10.1.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Resistivity;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.10.1.weighting=1@
qu.10.1.numbering=alpha@
qu.10.1.part.1.name=sro_id_1@
qu.10.1.part.1.answer.units=@
qu.10.1.part.1.numStyle= scientific  @
qu.10.1.part.1.editing=useHTML@
qu.10.1.part.1.showUnits=false@
qu.10.1.part.1.question=(Unset)@
qu.10.1.part.1.mode=Numeric@
qu.10.1.part.1.grading=exact_sigd@
qu.10.1.part.1.negStyle=both@
qu.10.1.part.1.digit=3@
qu.10.1.part.1.answer.num=$ans@
qu.10.1.question=<p align="left">A particular Ohmic wire&nbsp;of length <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mstyle></math>&nbsp;and cross-sectional area <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$A</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msup><mi>mm</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math>&nbsp;has unknown resistivity.<br />If a&nbsp;potential&nbsp;difference&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Vex</mi></mrow></msup><mi>V</mi></mrow></mstyle></math>&nbsp;produces a current of&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>, what is the resistivity of the wire, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Omega;</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>m</mi></mrow></mstyle></math>?</p><p align="left">&nbsp;</p><p align="left"><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&Omega;</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>m</mi></mrow></mstyle></math></span></p>@

qu.10.2.mode=Inline@
qu.10.2.name=Resistivity - Find Area ~ NG@
qu.10.2.comment=@
qu.10.2.editing=useHTML@
qu.10.2.solution=<p>Resistance is related to resistivity by:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>&rho;L</mi><mrow><mi>A</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given the current and the potential difference, thus we can find the resistance using Ohm's Law.</p>
<p>So,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>&rho;LI</mi><mrow><mi>V</mi></mrow></mfrac></mrow></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$rho</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>&Omega;</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>m</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mfenced></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mV</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math></p>@
qu.10.2.algorithm=$V=rand(1.00,9.99,3);
$L=rand(1.00,9.99,3);
$rho=2.44*10^(-8);
$I=rand(1.00,9.99,3);
$ans=$rho*($L*10^(-3))*$I/($V*10^(-3));@
qu.10.2.uid=b84ca163-8e6c-4c77-8d2c-4df613a35a89@
qu.10.2.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Resistivity;
  Difficulty=Easy;
  Features=Algorithmic;
@
qu.10.2.weighting=1@
qu.10.2.numbering=alpha@
qu.10.2.part.1.name=sro_id_1@
qu.10.2.part.1.answer.units=@
qu.10.2.part.1.numStyle= scientific  @
qu.10.2.part.1.editing=useHTML@
qu.10.2.part.1.showUnits=false@
qu.10.2.part.1.question=(Unset)@
qu.10.2.part.1.mode=Numeric@
qu.10.2.part.1.grading=exact_sigd@
qu.10.2.part.1.negStyle=both@
qu.10.2.part.1.digit=3@
qu.10.2.part.1.answer.num=$ans@
qu.10.2.question=<p align="left">A current of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>&nbsp;is passed through a&nbsp;gold wire&nbsp;of length <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mstyle></math>, resulting in a potential difference of<br />&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mV</mi></mrow></mstyle></math>&nbsp;between the two ends of the wire.&nbsp; If these measurements are made at room temperature,&nbsp;<br />what is the cross-sectional area of the wire, in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>m</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math>?</p><p align="left">&nbsp;</p><p align="left"><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>m</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math></span></p>@

qu.10.3.mode=Inline@
qu.10.3.name=Resistivity - Find Voltage ~ NG@
qu.10.3.comment=@
qu.10.3.editing=useHTML@
qu.10.3.solution=<p>Resistance is related to resistivity by:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>&rho;L</mi><mrow><mi>A</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given the&nbsp;current, thus we can&nbsp;replace the resistance using Ohm's Law to introduce potential difference.</p>
<p>So,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>I</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo></mrow><mrow><mfrac><mrow><mi>&rho;</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>L</mi></mrow><mrow><mi>A</mi></mrow></mfrac></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$rho</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$rhoex</mi></mrow></msup><mi>&Omega;</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>m</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfenced></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$A</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msup><mi>mm</mi><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.10.3.algorithm=$L=rand(1.00,9.99,3);
$rho=rand(1.00,9.99,3);
$rhoex=range(6,9);
$I=rand(1.00,9.99,3);
$A=rand(0.100,0.999,3);
$ans=($rho*10^(-$rhoex))*($L*10^(-3))*$I/($A*10^(-6));@
qu.10.3.uid=88f85606-ec05-4bd0-b91a-9d1108bb6829@
qu.10.3.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Resistivity;
  Difficulty=Easy;
  Features=Algorithmic;
@
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qu.10.3.part.1.question=(Unset)@
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qu.10.3.question=<p align="left">A particular wire&nbsp;of length <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mstyle></math>&nbsp;and cross-sectional area <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$A</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msup><mi>mm</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math>&nbsp;has resistivity <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$rho</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$rhoex</mi></mrow></msup><mi>&Omega;</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>m</mi></mrow></mstyle></math>.<br />What potential&nbsp;difference (in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math>) must there be between the ends of the&nbsp;length of wire to cause<br />a&nbsp;current&nbsp;of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$I</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi></mrow></mstyle></math>&nbsp;to pass through it?</p><p align="left"><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>V</mi></mrow></mstyle></math></span></p>@

qu.10.4.mode=Inline@
qu.10.4.name=Resistivity - Find Current ~ NG@
qu.10.4.comment=@
qu.10.4.editing=useHTML@
qu.10.4.solution=<p>Resistance is related to resistivity by:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>R</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>&rho;L</mi><mrow><mi>A</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>
<p>We are given the&nbsp;potential difference, thus we can&nbsp;replace the resistance using Ohm's Law to introduce current.</p>
<p>So,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>I</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>V</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>A</mi></mrow><mrow><mi>&rho;</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>L</mi></mrow></mfrac></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>I</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Vex</mi></mrow></msup><mi>V</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$A</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msup><mi>mm</mi><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi>$rho</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$rhoex</mi></mrow></msup><mi>&Omega;</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>m</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mfenced></mrow></mfrac></mrow></mstyle></math>.</p>@
qu.10.4.algorithm=$L=rand(1.00,9.99,3);
$rho=rand(1.00,9.99,3);
$rhoex=range(6,9);
$A=rand(0.100,0.999,3);
$V=rand(1.00,9.99,3);
$Vex=range(1,5);
$ans=($V*10^(-$Vex))*($A*10^(-6))/($rho*10^(-$rhoex))*($L*10^(-3));@
qu.10.4.uid=6d0b335c-6faf-4b95-b7eb-15b684a28156@
qu.10.4.info=  Course=Introductory Electricity and Magnetism;
  Author=Aron Pasieka;
  Topic=Resistivity;
  Difficulty=Easy;
  Features=Algorithmic;
@
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qu.10.4.question=<p align="left">A particular wire&nbsp;of length <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$L</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>mm</mi></mrow></mstyle></math>&nbsp;and cross-sectional area <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$A</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msup><mi>mm</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math>&nbsp;has resistivity <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$rho</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$rhoex</mi></mrow></msup><mi>&Omega;</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>m</mi></mrow></mstyle></math>.<br />If a&nbsp;potential&nbsp;difference&nbsp;of&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>$V</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&times;</mo><msup><mn>10</mn><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$Vex</mi></mrow></msup><mi>V</mi></mrow></mstyle></math>&nbsp;is applied across the wire, what is the resulting current,&nbsp;<br />in <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math>?</p><p align="left"><1><span>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi></mrow></mstyle></math></span></p>@

