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<p> This week we are looking at a new concept we call Electric Potential. The Electric Potential relates to the Electric Potential Energy in the same way that the Electric Field relates to the Electric Force. To begin, we will present one way to calculate and think about the Electric Potential Difference. In the next few lessons we then explore its connection to work, what happens when we set a zero point, and how to calculate the Potential for a variety of charge distributions.</p><p> Textbook Links </p><ul><li><a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/4/8">Chapter 4.2 Electric Potential in a Uniform Field</a></li></ul>
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<h2 class="hd hd-2 unit-title">L7v1: Electric Potential Difference</h2>
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<h3 class="hd hd-2">L07v01: Electric Potential Difference</h3>
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<h2 class="hd hd-2 unit-title">L7Q1: Electric Potential Difference</h2>
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Electric Potential Difference
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Which of the following statements are true about the electric potential difference. </p>
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<text>The electric potential difference is positive for a positive test charge and negative for a negative test charge.</text>
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<text>The electric potential difference between two points in space can be calculated as the negative path integral of the electric field between those points.</text>
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<text>The electric potential difference points in the same direction as the electric field.</text>
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<text>The definition of the electric potential difference is related to the work done by the electric field.</text>
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<h2 class="hd hd-2 unit-title">L7v2: Potential Difference of Two Parallel Plates</h2>
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Electric Potential Difference Between Parallel Non-Conducting Charged Plates
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Two parallel infinite non-conducting plates lying in the <i class="itshape">xy</i>-plane are separated by a distance [mathjaxinline]d[/mathjaxinline]. The upper plate, located at [mathjaxinline]z=d/2[/mathjaxinline], is uniformly charged with surface charge density [mathjaxinline]+\sigma[/mathjaxinline]. The lower plate located at [mathjaxinline]z=-d/2[/mathjaxinline] is uniformly charged with surface charge density [mathjaxinline]-\sigma[/mathjaxinline]. See the diagram below. </p>
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<img src="/assets/courseware/v1/e7a06a035cb96ad782dadfe57eb7396e/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_Spring_2014_pset04_5-fig001.png" width="440"/>
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<p><b class="bfseries">(Part a)</b> Find the component of the electric field in the [mathjaxinline]z[/mathjaxinline] direction in the following regions. Express your answer using epsilon_0 for [mathjaxinline]\varepsilon _{0}[/mathjaxinline], sigma for [mathjaxinline]\sigma[/mathjaxinline], and [mathjaxinline]d[/mathjaxinline] as needed. </p>
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(i) [mathjaxinline]z&gt;d/2[/mathjaxinline] </p>
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<p style="display:inline">[mathjaxinline]E_ z =[/mathjaxinline] </p>
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(ii) [mathjaxinline]-d/2&lt;z&lt;d/2[/mathjaxinline] </p>
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<p style="display:inline">[mathjaxinline]E_ z =[/mathjaxinline] </p>
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(iiI) [mathjaxinline]z&lt;-d/2[/mathjaxinline] </p>
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<p style="display:inline">[mathjaxinline]E_ z =[/mathjaxinline] </p>
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<p><b class="bfseries">(Part b)</b> Find the electric potential difference [mathjaxinline]\Delta V = V(d/2)-V(-d/2)[/mathjaxinline]. Express your answer using epsilon_0 for [mathjaxinline]\varepsilon _{0}[/mathjaxinline], sigma for [mathjaxinline]\sigma[/mathjaxinline], and [mathjaxinline]d[/mathjaxinline] as needed. </p>
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<p style="display:inline">[mathjaxinline]\Delta V =[/mathjaxinline] </p>
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<h2 class="hd hd-2 unit-title">L7Q2: Changing Distance Between Parallel Plates</h2>
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Changing Distance Between Parallel Plates
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Two parallel infinite non-conducting plates lying in the <i class="itshape">xy</i>-plane are separated by a distance [mathjaxinline]d[/mathjaxinline]. The upper plate, located at [mathjaxinline]z=d/2[/mathjaxinline], is uniformly charged with surface charge density [mathjaxinline]+\sigma[/mathjaxinline]. The lower plate located at [mathjaxinline]z=-d/2[/mathjaxinline] is uniformly charged with surface charge density [mathjaxinline]-\sigma[/mathjaxinline]. See the diagram below. </p>
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<img src="/assets/courseware/v1/e7a06a035cb96ad782dadfe57eb7396e/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_Spring_2014_pset04_5-fig001.png" width="440"/>
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Initially the potential difference between these plates is given by [mathjaxinline]\Delta V_{0}[/mathjaxinline]. If the distance between the plates is increased from [mathjaxinline]d[/mathjaxinline] to [mathjaxinline]3d[/mathjaxinline], leaving the charge on the plates the same, what is the new value of the potential difference between the plates. Express your answer in terms of DeltaV_0 for [mathjaxinline]\Delta V_{0}[/mathjaxinline]. </p>
<p>
<p style="display:inline">[mathjaxinline]\Delta V =[/mathjaxinline] </p>
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<h2 class="hd hd-2 unit-title">L7Q3: Difference in Potential</h2>
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Difference in potential
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<p>
A thin and non conducting cylindrical shell of radius [mathjaxinline]a[/mathjaxinline] is uniformly charged with a surface charge density [mathjaxinline]\sigma &lt;0[/mathjaxinline]. Assume the shell is infinite in length. A cross section of the shell is shown in the right figure. Consider the three points: [mathjaxinline]A[/mathjaxinline] at [mathjaxinline]r=a/2[/mathjaxinline], [mathjaxinline]B[/mathjaxinline] at [mathjaxinline]r=a[/mathjaxinline], and [mathjaxinline]C[/mathjaxinline] at [mathjaxinline]r=2a[/mathjaxinline] from the axis of the shell. </p>
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Which of the statements below about the difference in potential between the points is true? </p>
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<text>[mathjaxinline]V(B)-V(A)&gt;0[/mathjaxinline]</text>
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<text>[mathjaxinline]V(B)-V(A)=0[/mathjaxinline]</text>
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<text>[mathjaxinline]V(B)-V(A)&lt;0[/mathjaxinline]</text>
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<text>[mathjaxinline]V(C)-V(B)&gt;0[/mathjaxinline]</text>
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<text>[mathjaxinline]V(C)-V(B)=0[/mathjaxinline]</text>
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<text>[mathjaxinline]V(C)-V(B)&lt;0[/mathjaxinline]</text>
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<text>[mathjaxinline]V(C)-V(A)&gt;0[/mathjaxinline]</text>
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<text>[mathjaxinline]V(C)-V(A)=0[/mathjaxinline]</text>
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<text>[mathjaxinline]V(C)-V(A)&lt;0[/mathjaxinline]</text>
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