---
title: "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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url: "https://nerd-notes.com/ubq/124900/"
date_modified: "2026-09-28T14:11:52+00:00"
---

# 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?

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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604712-AbqjFZ.jpg)

- **A.** \(\displaystyle \int_a^b \dfrac{Q^2}{2\pi \varepsilon_0 L r} \, dr\)
- **B.** \(\displaystyle \int_a^b \dfrac{Q^2}{4\pi \varepsilon_0 L r} \, dr\)
- **C.** \(\displaystyle \int_0^b \dfrac{Q^2}{4\pi \varepsilon_0 L r} \, dr\)
- **D.** \(\displaystyle \int_a^b \dfrac{Q^2}{2\pi \varepsilon_0 L^2} \, dr\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124900/*