AP Physics C E and M 9.3 Potential Difference Overview

Analyze how potential differences change the energy and motion of charged systems, connecting electric work with conservation of electric energy.

[Maximum number: 4]

A nonconducting rod of uniform positive linear charge density is near a sphere with charge -2.0 nC. The rod and sphere are held at rest on the x-axis, as shown in Figure 1. Equipotential lines and positions A, B, C, D, and E are labeled. Adjacent tick marks on the x-axis and the y-axis are 0.40 m apart.

The bar shown in Figure 2 represents the absolute value of the work $W_{\mathrm{CE}}$ done by the external force on the test charge to move the test charge from Position C to Position E.

Complete the following tasks on Figure 2.

- Draw a bar to represent the relative absolute value of the work $W_{\mathrm{ED}}$ done by the external force on the test charge to move the test charge from Position E to Position D.

- Draw a bar to represent the relative absolute value of the work $W_{\mathrm{DA}}$ done by the external force on the test charge to move the test charge from Position D to Position A.

- The height of each bar should be proportional to the value of $W_{\mathrm{CE}}$ . If $W_{\mathrm{ED}}=0$ and/or $W_{\mathrm{DA}}=0$ , write a "0" in the corresponding columns, as appropriate.

Figure 2

Calculate the approximate magnitude of the x-component of the electric field at Position B.

The positive test charge is placed at Position D. The test charge is then released from rest.

For indicating that $W_{\mathrm{ED}}=0$

1 point

For drawing a bar representing $W_{\mathrm{DA}}$ that has a height of six units

1 point
Example Response

Figure for Answer to Question 9.3 Conservation of Electric Energy question 1 — AP Physics C: Electricity & Magnetism

Scoring Note: This point can be earned if the response begins with a correct relationship between electric field and potential difference in which numerical values are already substituted.

Example Responses

E_{x}=-\frac{d V}{d x} \quad \mathbf{O R} \quad\left|E_{x}\right|=\left|-\frac{d V}{d x}\right| \quad \mathbf{O R} \quad\left|E_{x}\right|=\left|-\frac{\Delta V}{\Delta x}\right| \quad \mathbf{O R} \quad \Delta V=-\int \vec{E} \cdot d \vec{r}

For correct substitutions of values of electric potential and the distance between equipotential 1 point lines that can be used to calculate the approximate magnitude of the electric field at Position B

Example Response

\left|E_{x}\right|=\left|-\frac{20.0 \mathrm{~V}-0.0 \mathrm{~V}}{0.65 \mathrm{~m}}\right|

Example Solution

\begin{aligned} & E_{x}=-\frac{d V}{d x} \\ & \left|E_{x}\right|=\left|-\frac{d V}{d x}\right| \\ & \left|E_{x}\right|=\left|-\frac{\Delta V}{\Delta x}\right| \\ & \left|E_{x}\right|=\left|-\frac{20.0 \mathrm{~V}-0.0 \mathrm{~V}}{0.65 \mathrm{~m}}\right| \\ & \left|E_{x}\right|=31 \frac{\mathrm{~V}}{\mathrm{~m}} \end{aligned}

Total for part (b) 4 points

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Covered syllabus points

9.3 Conservation of Electric Energy question 1