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AP Physics C: Electricity & Magnetism 8.4 Electric Fields of Charge Distributions Questions

Determine electric fields from continuous charge distributions by modeling charge density, geometry, symmetry, and integrated field contributions.

Syllabus
Effective Fall 2024
Course
AP Physics C: Electricity & Magnetism

Exam points

  • express a charge element or total charge from linear density with correct variables and limits
  • use symmetry to cancel field components and determine the surviving field direction
  • set up and evaluate a Coulomb-law integral for a finite wire, ring, or circular arc
  • take a far-field limit and recover the point-charge field of the distribution's total charge
  • interpret or sketch field, acceleration, or velocity variation with position near a distribution

Covered syllabus points

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).

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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