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💡AP Physics C: Electricity and Magnetism
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💡AP Physics C: Electricity and Magnetism

FRQ 1 – Mathematical Routines
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Unit 8: Electric Charges, Fields, and Gauss's Law
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Practice FRQ 1 of 201/20

1. An isolated spherical capacitor is constructed from two thin, concentric conducting shells. The inner shell has radius R1 = 0.040 m and the outer shell has radius R2 = 0.120 m, as shown in Figure 1. The inner shell has a total charge +Q = +6.0 nC placed on it, and the outer shell has a total charge −Q = −6.0 nC. The space between the shells is air (permittivity ε0). Assume electrostatic equilibrium and that the shells are very thin compared with their radii.

Figure 1. Isolated spherical capacitor

Figure 1

Figure 2. Axes for electric field magnitude

Figure 2
A.
i.

Using Gauss’s law, derive an expression for the magnitude E of the electric field as a function of the radial distance r from the center of the capacitor for the region R1 < r < R2. Express your answer in terms of Q, r, and physical constants, as appropriate.

ii.

Derive an expression for the absolute value ΔV of the potential difference between the outer and inner shells in terms of Q, R1, R2, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii.

On the axes shown in Figure 2, sketch a graph of E as a function of r from r = 0 to a position that is outside the outer shell.

Figure 3. Spherical capacitor with dielectric

Figure 3
B.

Derive an expression for the capacitance C of the capacitor with the dielectric inserted in terms of R1, R2, κ, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. A dielectric material with dielectric constant κ = 3.5 is inserted into the isolated, charged capacitor such that it fills the region R1 < r < R2, as shown in Figure 3.

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Free Response Question Practice

This practice environment simulates the AP AP Physics C: Electricity and Magnetism Free Response Questions section. Here are some guidelines:

  • Read each question carefullybefore responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
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Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.