2024 AP Physics C: Electricity and Magnetism Free-Response Questions

Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part. Figure 1 1. 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. (a) Calculate the absolute value of the electric flux through the Gaussian surface whose cross section is the −20.0 V equipotential line. A positive test charge (not shown) is placed and held at rest at Position C. An external force is applied to the test charge to move the test charge to different positions in the order of C→E→D→A. The test charge is momentarily held at rest at each position. (b) The bar shown in Figure 2 represents the absolute value of the work W_CE done by the external force on the test charge to move the test charge from Position C to Position E. i. Complete the following tasks on Figure 2. • Draw a bar to represent the relative absolute value of the work W_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_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_CE. If W_ED = 0 and/or W_DA = 0, write a "0" in the corresponding columns, as appropriate. Figure 2 ii. 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. (c) Indicate the direction (not components) of the net electric force exerted on the test charge immediately after the test charge is released from rest. ___ +x ___ +y ___ Directly away from the sphere ___ −x ___ −y ___ Directly toward the sphere Without using equations, justify your answer using physics principles. Figure 3 The sphere and the test charge are removed. The rod has length 4L and uniform positive linear charge density +λ. The rod is held at rest on the x-axis in the orientation shown in Figure 3. Position P (not shown) is located on the x-axis a distance x_P from the origin, where x_P > 4L. (d) The electric potential V_P at x_P is V_P = kλ ln ( x_P / (x_P − 4L) ). i. Using integral calculus, derive the expression for V_P provided. ii. On Figure 4, sketch a graph of the x-component E_x of the electric field from the rod as a function of x in the region 4L < x < 12L. Figure 4