---
title: "A cylindrical capacitor consists of two long, coaxial conducting cylindrical shells of inner radius \\(a\\) and outer radius \\(b\\) separated by vacuum. The inner shell carries a uniform linear charge density \\(+\\lambda\\) and the outer shell carries a uniform linear charge density \\(-\\lambda\\). Which of the following expressions is equal to the capacitance per unit length of the cylindrical capacitor?"
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url: "https://nerd-notes.com/ubq/121153/"
date_modified: "2026-08-23T04:58:18+00:00"
---

# A cylindrical capacitor consists of two long, coaxial conducting cylindrical shells of inner radius \(a\) and outer radius \(b\) separated by vacuum. The inner shell carries a uniform linear charge density \(+\lambda\) and the outer shell carries a uniform linear charge density \(-\lambda\). Which of the following expressions is equal to the capacitance per unit length of the cylindrical capacitor?

A cylindrical capacitor consists of two long, coaxial conducting cylindrical shells of inner radius \(a\) and outer radius \(b\) separated by vacuum. The inner shell carries a uniform linear charge density \(+\lambda\) and the outer shell carries a uniform linear charge density \(-\lambda\). Which of the following expressions is equal to the capacitance per unit length of the cylindrical capacitor?

![A cross-sectional view of two concentric circles centered at the origin. The inner circle has a solid boundary with a dashed arrow pointing from the origin to its edge labeled a. The outer circle has a solid boundary with a dashed arrow pointing from the origin to its edge labeled b. The region between the inner and outer circles is unfilled white space. A plus symbol labeled +\lambda is located inside the inner circle, and a minus symbol labeled -\lambda is located just outside the outer circle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461098-R5EPf6.jpg)

- **A.** \(\dfrac{2\pi\varepsilon_0}{\ln(b/a)}\)
- **B.** \(\dfrac{4\pi\varepsilon_0}{\ln(b/a)}\)
- **C.** \(\dfrac{2\pi\varepsilon_0 a}{b-a}\)
- **D.** \(\dfrac{\pi\varepsilon_0}{\ln(b/a)}\)

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