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<p> Now that we know how to calculate the electric potential difference, we take a step back and see how it fits into the ideas of work and potential energy difference.</p><p> Textbook Links </p><ul><li><a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/4/2">Chapter 4.1-4.3 Electric Potential</a></li></ul>
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<h2 class="hd hd-2 unit-title">L8v1: Potential and Potential Energy</h2>
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<h2 class="hd hd-2 unit-title">L8Q1: Units</h2>
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Electric Potential Energy: Units
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<p>Which of the following are possible units of electric potential energy?</p>
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<text>a) Newtons/Coulomb</text>
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<text>b) Joules</text>
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<text>c) Volt-Coulombs</text>
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<text>d) Newton-Meters</text>
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<text>e) Volts</text>
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<text>f) Kilowatt-Hours</text>
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<text>g) Newton-Meters/Coulomb</text>
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Electric Potential: Units
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<p>Which of the following are possible units of electric potential?</p>
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<text>a) Newtons/Coulomb</text>
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<input type="checkbox" name="input_pcq_w3d2d_2_1[]" id="input_pcq_w3d2d_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="pcq_w3d2d_2_1-choice_1-label" for="input_pcq_w3d2d_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pcq_w3d2d_2_1">
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<text>c) Volt-Coulombs</text>
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<text>d) Newton-Meters</text>
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<text>e) Volts</text>
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<text>f) Kilowatt-Hours</text>
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<text>g) Newton-Meters/Coulomb</text>
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<h2 class="hd hd-2 unit-title">L8v2: Work for a Moving Point Charge</h2>
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<h2 class="hd hd-2 unit-title">Review of Conservative Forces</h2>
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<p><b>Conservative Forces. </b></p><p><center><img src="/assets/courseware/v1/72c019bb3708919c0c6c53119027110e/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_html_lesson07_01.svg" width="600"/></center></p><p>If the work done by a force in moving an object from point \(A\) to point \(B\) is <b>independent of the path</b>, then the force is called a <b>conservative force</b>. </p><p>As a result, the work done by the conservative force only depends on the location of the points \(A\) and \(B\).</p><p> Equivalent definition of a conservative force:</p><p><center><img src="/assets/courseware/v1/8790402af0b61f04f234b0de2c970947/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_html_lesson07_02.svg" width="600"/></center></p><p> The work done by a conservative force to move an object along a closed path is zero.</p>
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<h2 class="hd hd-2 unit-title">L8Q2: A Moving Point Charge</h2>
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A moving point charge.
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<p><b class="bfseries">(Part a)</b> A point like object of charge [mathjaxinline]q_1&gt;0[/mathjaxinline] is fixed in space. Calculate [mathjaxinline]W_{A,B}[/mathjaxinline], the work done by the electric field produced by [mathjaxinline]q_1[/mathjaxinline] on a second point like object of charge [mathjaxinline]q_2 &gt;0[/mathjaxinline] when it moves from point [mathjaxinline]A[/mathjaxinline] to point [mathjaxinline]B[/mathjaxinline]. Point [mathjaxinline]A[/mathjaxinline] is at a distance [mathjaxinline]2R[/mathjaxinline] from [mathjaxinline]q_1[/mathjaxinline] and point [mathjaxinline]B[/mathjaxinline] is at a distance [mathjaxinline]R[/mathjaxinline] from [mathjaxinline]q_1[/mathjaxinline]. Express your answer in terms of the Coulomb constant [mathjaxinline]k[/mathjaxinline], [mathjaxinline]R[/mathjaxinline], q_1 for [mathjaxinline]q_1[/mathjaxinline], and q_2 for [mathjaxinline]q_2[/mathjaxinline] as needed. </p>
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<p style="display:inline">[mathjaxinline]W_{A,B}=[/mathjaxinline]</p>
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<p><b class="bfseries">(Part b)</b> Calculate [mathjaxinline]W_{B,C}[/mathjaxinline], the work done by the electric field produced by [mathjaxinline]q_1[/mathjaxinline] on [mathjaxinline]q_2[/mathjaxinline], when charge [mathjaxinline]q_2[/mathjaxinline] moves along the circular arc of radius [mathjaxinline]R[/mathjaxinline] from point [mathjaxinline]B[/mathjaxinline] to [mathjaxinline]C[/mathjaxinline]. Express your answer in terms of the Coulomb constant [mathjaxinline]k[/mathjaxinline], [mathjaxinline]R[/mathjaxinline], q_1 for [mathjaxinline]q_1[/mathjaxinline], and q_2 for [mathjaxinline]q_2[/mathjaxinline] as needed. </p>
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<p style="display:inline">[mathjaxinline]W_{B,C}=[/mathjaxinline]</p>
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<p><b class="bfseries">(Part c)</b> Calculate [mathjaxinline]W_{C,D}[/mathjaxinline], the work done by the electric field produced by [mathjaxinline]q_1[/mathjaxinline] on [mathjaxinline]q_2[/mathjaxinline], when [mathjaxinline]q_2[/mathjaxinline] moves from point [mathjaxinline]C[/mathjaxinline] a distance to point [mathjaxinline]D[/mathjaxinline]. Point [mathjaxinline]D[/mathjaxinline] is at a distance [mathjaxinline]2R[/mathjaxinline] from [mathjaxinline]q_1[/mathjaxinline]. Express your answer in terms of the Coulomb constant [mathjaxinline]k[/mathjaxinline], [mathjaxinline]R[/mathjaxinline], q_1 for [mathjaxinline]q_1[/mathjaxinline], and q_2 for [mathjaxinline]q_2[/mathjaxinline] as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]W_{C,D}=[/mathjaxinline]</p>
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<p><b class="bfseries">(Part d)</b> Calculate [mathjaxinline]W_{D,A}[/mathjaxinline], the work done by the electric field produced by [mathjaxinline]q_1[/mathjaxinline] on [mathjaxinline]q_2[/mathjaxinline], when charge [mathjaxinline]q_2[/mathjaxinline] moves along the circular arc of radius [mathjaxinline]2R[/mathjaxinline] from point [mathjaxinline]D[/mathjaxinline] to [mathjaxinline]A[/mathjaxinline]. Express your answer in terms of the Coulomb constant [mathjaxinline]k[/mathjaxinline], [mathjaxinline]R[/mathjaxinline], q_1 for [mathjaxinline]q_1[/mathjaxinline], and q_2 for [mathjaxinline]q_2[/mathjaxinline] as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]W_{D,A}=[/mathjaxinline]</p>
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<p><b class="bfseries">(Part e)</b> Calculate [mathjaxinline]W_{A,A}[/mathjaxinline], the work done by the electric field produced by [mathjaxinline]q_1[/mathjaxinline] on [mathjaxinline]q_2[/mathjaxinline], when charge [mathjaxinline]q_2[/mathjaxinline] moves from point [mathjaxinline]A[/mathjaxinline] back to point [mathjaxinline]A[/mathjaxinline], following the path indicated in the figure. Express your answer in terms of the Coulomb constant [mathjaxinline]k[/mathjaxinline], [mathjaxinline]R[/mathjaxinline], q_1 for [mathjaxinline]q_1[/mathjaxinline], and q_2 for [mathjaxinline]q_2[/mathjaxinline] as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]W_{A,A}=[/mathjaxinline]</p>
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<h2 class="hd hd-2 unit-title">L8Q3: Work by the Field</h2>
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<h3 class="hd hd-3 problem-header" id="pcq_w3d2e-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w3d2e-problem-progress" tabindex="-1">
Work by the Field
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<p>An isolated point-like positively charged object with charge [mathjaxinline]q_s&gt;0[/mathjaxinline] is at the origin. You move a point-like negatively charged object with charge [mathjaxinline]q_1&lt;0[/mathjaxinline] at a constant speed from [mathjaxinline]\vec{\mathbf{r}}_{\rm A}[/mathjaxinline] to [mathjaxinline]\vec{\mathbf{r}}_{\rm B}[/mathjaxinline] where [mathjaxinline]|\vec{\mathbf{r}}_{\rm A}| &lt; |\vec{\mathbf{r}}_{\rm B}|[/mathjaxinline]. Have you done positive or negative work? Has the electric field done positive or negative work?</p>
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<text>Negative work by you; positive work by the field</text>
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<text>Negative work by you; negative work by the field</text>
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<text>Positive work by you; negative work by the field</text>
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<text>Positive work by you; positive work by the field</text>
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<h2 class="hd hd-2 unit-title">L8v3: Sign of Work</h2>
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<h3 class="hd hd-2">L08v03: Sign of Work</h3>
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<h2 class="hd hd-2 unit-title">L8v4: Potential for a Point Charge</h2>
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<h3 class="hd hd-2">L08v04: Potential for a Point Charge</h3>
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<h2 class="hd hd-2 unit-title">L8Q4: Potential Difference from Infinity</h2>
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Potential Difference from Infinity
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<p>An isolated positively charged point-like object with charge [mathjaxinline]q_s&gt;0[/mathjaxinline] is at the origin. Consider two points A and B, where [mathjaxinline]|\vec{\mathbf{r}}_{\rm A}| &lt; |\vec{\mathbf{r}}_{\rm B}|[/mathjaxinline].</p>
<p>Consider the electric potential difference due to the source charge \(q_s\) from infinity to [mathjaxinline]\vec{\mathbf{r}}_{\rm A}[/mathjaxinline] to be \(50\) V. Which of the following statements is/are true?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pcq_w3d2f_2_1">
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<text>a) If a negatively charged point-like object is moved from A to B then the electric potential energy of the system of the two charged obejcts increases.</text>
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<text>b) The electric potential difference from infinity to B is bigger than the potential difference from infinity to A.</text>
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<text>c) If the distance between \(q_s\) and B is 2 times the distance between \(q_s\) and A, the electric potential difference from infinity to B is 1/4 the electric potential difference from infinity to A.</text>
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<text>d) The electric potential energy of an electron at A is [mathjaxinline]-50 \, eV[/mathjaxinline].</text>
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