---
title: "A long coaxial cable consists of a thin cylindrical inner conductor of radius \\(a\\) and a thin coaxial outer conducting shell of radius \\(b\\). Equal and opposite currents \\(I\\) flow uniformly along the inner and outer conductors. Which of the following expressions represents the self-inductance per unit length \\(L/\\ell\\) of the coaxial cable?"
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url: "https://nerd-notes.com/ubq/118681/"
date_modified: "2026-08-04T08:13:44+00:00"
---

# A long coaxial cable consists of a thin cylindrical inner conductor of radius \(a\) and a thin coaxial outer conducting shell of radius \(b\). Equal and opposite currents \(I\) flow uniformly along the inner and outer conductors. Which of the following expressions represents the self-inductance per unit length \(L/\ell\) of the coaxial cable?

A long coaxial cable consists of a thin cylindrical inner conductor of radius \(a\) and a thin coaxial outer conducting shell of radius \(b\). Equal and opposite currents \(I\) flow uniformly along the inner and outer conductors. Which of the following expressions represents the self-inductance per unit length \(L/\ell\) of the coaxial cable?

![A cross-sectional view of two concentric circular conductors. An inner solid circle of radius \(a\) is centered at the origin, shaded light gray, with a dot at its center indicating current pointing out of the page labeled \(I\). An outer circular shell of inner radius \(b\) is concentric with the inner circle, shaded light gray, containing an 'X' symbol indicating current \(I\) pointing into the page. The region between radius \(a\) and radius \(b\) is unshaded white space. A dashed radial line segment extends from the center to the outer edge of the inner conductor, labeled \(a\). A second dashed radial line segment extends from the center to the inner edge of the outer conductor, labeled \(b\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831223-RVf36T.jpg)

- **A.** \(\dfrac{\mu_0}{4\pi} \ln\left(\dfrac{b}{a}\right)\)
- **B.** \(\dfrac{\mu_0}{2\pi} \ln\left(\dfrac{b}{a}\right)\)
- **C.** \(\dfrac{\mu_0}{2\pi} \left(\dfrac{b-a}{a}\right)\)
- **D.** \(\dfrac{\mu_0}{2\pi} \ln\left(\dfrac{b+a}{a}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118681/*