Electrostatic Potential and Capacitance — Practice

Question 1

Charges 2 uC and -2 uC are 0.1 m apart. Find the potential at the midpoint.

Accepted Answer

V = k(2e-6)/0.05 + k(-2e-6)/0.05 = 0; the potential at the midpoint of a dipole is zero.

Question 2

A parallel plate capacitor has area 0.1 m^2 and separation 1 mm. Find its capacitance.

Accepted Answer

C = epsilon0 A / d = 8.85e-12 x 0.1 / 1e-3 = 8.85e-10 F = 885 pF.

Question 3

Find the equivalent capacitance of 4, 6, 12 uF in parallel and the charge stored at 10 V.

Accepted Answer

C_eq = 4 + 6 + 12 = 22 uF. Q = CV = 22e-6 x 10 = 220 uC.

Question 4

A 10 uF capacitor charged to 100 V is connected to an uncharged 10 uF capacitor. Find the energy loss.

Accepted Answer

Initial energy = 0.5 x 10e-6 x 100^2 = 0.05 J. Charge Q = 1e-3 C, combined C = 20 uF, V' = 50 V. Final energy = 0.5 x 20e-6 x 50^2 = 0.025 J. Loss = 0.025 J (dissipated).

Question 5

A dielectric K = 3 is inserted in a 5 uF capacitor charged to 20 V with the battery disconnected. Find new C, V, and energy.

Accepted Answer

C' = 3 x 5 = 15 uF. Q stays 100 uC, so V' = 100/15 = 6.67 V. U' = 0.5 Q^2/C' = 3.33e-4 J, down from 5e-4 J.

Practice — Electrostatic Potential and Capacitance

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