---
title: "A long, hollow cylindrical conductor has an inner radius \\(a\\) and an outer radius \\(b\\). A total current \\(I\\) is distributed uniformly across the conductor’s cross-sectional area between \\(r = a\\) and \\(r = b\\), flowing parallel to the central axis. Which of the following expressions gives the magnitude of the magnetic field \\(B(r)\\) at a radial distance \\(r\\) from the central axis in the region \\(a < r < b\\)?"
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url: "https://nerd-notes.com/ubq/118516/"
date_modified: "2026-08-04T08:11:12+00:00"
---

# A long, hollow cylindrical conductor has an inner radius \(a\) and an outer radius \(b\). A total current \(I\) is distributed uniformly across the conductor’s cross-sectional area between \(r = a\) and \(r = b\), flowing parallel to the central axis. Which of the following expressions gives the magnitude of the magnetic field \(B(r)\) at a radial 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 distributed uniformly across the conductor's cross-sectional area between \(r = a\) and \(r = b\), flowing parallel to the central axis. Which of the following expressions gives the magnitude of the magnetic field \(B(r)\) at a radial distance \(r\) from the central axis in the region \(a < r < b\)?

![A cross-sectional view of a long cylindrical conductor centered at the origin. An inner circle of radius \(a\) is centered at the origin and left unshaded. An outer circle of radius \(b\), concentric with the inner circle, defines the outer boundary of the conductor. The region between radius \(a\) and radius \(b\) is shaded light gray to represent the conductor material, containing several evenly spaced dot symbols pointing out of the page to represent uniform current flow. A concentric dashed circular line of radius \(r\), where \(a < r < b\), represents a circular Amperian loop. A radial line extending from the origin to this dashed loop is labeled \(r\). Straight radial lines from the center to the inner and outer circles are labeled \(a\) and \(b\), respectively. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831072-CEisik.jpg)

- **A.** \(\dfrac{\mu_0 I r}{2\pi (b^2 - a^2)}\)
- **B.** \(\dfrac{\mu_0 I (r - a)}{2\pi r (b - a)}\)
- **C.** \(\dfrac{\mu_0 I (r^2 - a^2)}{2\pi r (b^2 - a^2)}\)
- **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/118516/*