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AP Physics C E and M 8.4: Electric Field from Charge Distributions

Determine the electric field resulting from a continuous charge distribution by modeling charge density and integrating field contributions.

Syllabus
Effective Fall 2025
Course
AP Physics C: Electricity & Magnetism

8.4.A—Describe the electric field resulting from a given charge distribution question 1

[Maximum number: 2]

A nonconducting rod of uniform negative linear charge density is near a sphere with charge +1.0 nC. The rod and sphere are held at rest on the y-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 on the y-axis are 0.40 m apart.

The electric potential VPV_{\mathrm{P}} at yPy_{\mathrm{P}} is VP=−kλln⁡(yPyP−2L)V_{\mathrm{P}}=-k \lambda \ln \left(\frac{y_{\mathrm{P}}}{y_{\mathrm{P}}-2 L}\right).

ii. On Figure 4, sketch a graph of the y-component EyE_{y} of the electric field resulting from the rod as a function of y in the region 2 L<y<12 L.

Figure 4

Figure 4

Figure 1

Figure 1

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