---
title: "Two extremely long, parallel conducting cylinders, each of radius \\(R\\), are oriented parallel to each other with a center-to-center separation distance \\(d\\), where \\(d \\gg R\\). The two cylinders carry uniform linear charge densities of \\(+\\lambda\\) and \\(-\\lambda\\), respectively. Which of the following expressions represents the capacitance per unit length \\(C/L\\) of this two-cylinder system?"
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url: "https://nerd-notes.com/ubq/118270/"
date_modified: "2026-08-04T08:08:33+00:00"
---

# Two extremely long, parallel conducting cylinders, each of radius \(R\), are oriented parallel to each other with a center-to-center separation distance \(d\), where \(d \gg R\). The two cylinders carry uniform linear charge densities of \(+\lambda\) and \(-\lambda\), respectively. Which of the following expressions represents the capacitance per unit length \(C/L\) of this two-cylinder system?

Two extremely long, parallel conducting cylinders, each of radius \(R\), are oriented parallel to each other with a center-to-center separation distance \(d\), where \(d \gg R\). The two cylinders carry uniform linear charge densities of \(+\lambda\) and \(-\lambda\), respectively. Which of the following expressions represents the capacitance per unit length \(C/L\) of this two-cylinder system?

![A clean cross-sectional diagram showing two parallel conducting cylinders end-on in a two-dimensional plane. On the left is a circle of radius \(R\) labeled with charge density \(+\lambda\). On the right, separated horizontally by a center-to-center distance \(d\), is an identical circle of radius \(R\) labeled with charge density \(-\lambda\). A horizontal dashed line segment connects the center of the left circle to the center of the right circle, with a double-headed dimension arrow below it labeled \(d\). A radial line segment from the center of the left circle to its top edge is labeled with radius \(R\). A horizontal axis labeled \(x\) starts at the center of the left circle and points to the right toward the right circle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830912-8sG1VU.jpg)

- **A.** \(\dfrac{\pi \varepsilon_0}{2\ln(d/R)}\)
- **B.** \(\dfrac{2\pi \varepsilon_0}{\ln(d/R)}\)
- **C.** \(\dfrac{\pi \varepsilon_0}{\ln(d/R)}\)
- **D.** \(\dfrac{\pi \varepsilon_0}{\ln(d/(2R))}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118270/*