---
title: "A long, hollow cylindrical conductor has an inner radius \\(a\\) and an outer radius \\(b\\). A total current \\(I\\) is uniformly distributed over the cross section of the conductor and flows parallel to its central axis. Which of the following expressions gives the magnitude of the magnetic field \\(B(r)\\) as a function of distance \\(r\\) from the central axis in the region \\(a < r < b\\)?"
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url: "https://nerd-notes.com/ubq/118498/"
date_modified: "2026-08-04T08:11:05+00:00"
---

# A long, hollow cylindrical conductor has an inner radius \(a\) and an outer radius \(b\). A total current \(I\) is uniformly distributed over the cross section of the conductor and flows parallel to its central axis. Which of the following expressions gives the magnitude of the magnetic field \(B(r)\) as a function of distance \(r\) from the central axis in the region \(a < r < b\)?

A long, hollow cylindrical conductor has an inner radius \(a\) and an outer radius \(b\). A total current \(I\) is uniformly distributed over the cross section of the conductor and flows parallel to its central axis. Which of the following expressions gives the magnitude of the magnetic field \(B(r)\) as a function of distance \(r\) from the central axis in the region \(a < r < b\)?

![A cross-sectional view of a thick cylindrical shell centered at the origin. The inner boundary is a circle of radius a, and the outer boundary is a circle of radius b. The annular region between radius a and radius b is shaded light gray to represent the conductor. Dark circles with central dots are evenly spaced throughout the shaded annular region, indicating current flowing out of the page. A dashed concentric circle of radius r lies in the region between a and b, representing an Amperian loop. A double-headed arrow labeled a extends from the center to the inner boundary. A double-headed arrow labeled b extends from the center to the outer boundary. A double-headed arrow labeled r extends from the center to the dashed circle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831064-jaHGU9.jpg)

- **A.** \(\dfrac{\mu_0 I (r^2 - a^2)}{2\pi r (b^2 - a^2)}\)
- **B.** \(\dfrac{\mu_0 I r}{2\pi (b^2 - a^2)}\)
- **C.** \(\dfrac{\mu_0 I (r - a)}{2\pi r (b - a)}\)
- **D.** \(\dfrac{\mu_0 I (b^2 - r^2)}{2\pi r (b^2 - a^2)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118498/*