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Electricity and Magnetism

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Energy Contained Within the Field of a Cylindrical Capacitor

EANDM-B22JHH

Figure 1 depicts the cross-sectional view of a cylindrical capacitor of length $L = 10.0 \text{ cm}$, inner radius $a = 5.00 \text{ mm}$ and outer radius $b = 8.00 \text{ mm}$. The figure is not to scale.

Figure 1. “Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.”

If this capacitor is charged so that a potential difference of $V = 1.50 \text{ kV}$ exists between the inner and outer shells, how much energy is stored in the electric field surrounding the inner cylinder?

A

$U = 1.80 \text{ J}$

B

$U = 0.704 \text{ J}$

C

$U = 1.33 \times 10^{-5} \text{ J}$

D

$U = 2.66 \times 10^{-5} \text{ J}$