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AP Physics C: E&M
10.3 Capacitors
AdvancedMCQMathematicalConceptual19k
A perspective view of two concentric horizontal cylinders sharing a common horizontal dashed centerline. The inner cylinder is solid with a light gray fill, having a circular left face of radius labeled a, indicated by an arrow from the center to its top edge. The outer cylinder is a hollow thin-walled cylinder of larger radius labeled b, indicated by a vertical arrow from the center to its outer top edge. Both cylinders extend horizontally to the right across the same length, with a horizontal double-headed dimension line below them labeled L. A label +Q is positioned near the inner cylinder, and a label -Q is positioned near the outer cylinder. No other labels, lines, text, or axes appear.
Coaxial cylindrical capacitor of length \(L\) with inner radius \(a\) and outer radius \(b\).
A coaxial cable of length \(L\) consists of a solid inner conducting cylinder of radius \(a\) and a thin outer coaxial cylindrical conducting shell of radius \(b\), where \(L \gg b\).

The inner conductor carries a total charge \(+Q\), and the outer conductor carries a total charge \(-Q\).

Which of the following integral expressions correctly represents the total electrostatic potential energy stored in the electric field between the two conductors?

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