---
title: "A long, straight cylindrical conductor of radius \\(R\\) carries a uniform current density \\(J\\) directed parallel to its central axis. The conductor contains an off-axis cylindrical cavity of radius \\(a\\) running along its entire length, with central axis parallel to and displaced by a distance \\(d\\) from the main conductor’s central axis. Which of the following expressions correctly gives the magnitude of the magnetic field \\(B\\) at a point inside the cavity located at a distance \\(r\\) from the main conductor’s central axis?"
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url: "https://nerd-notes.com/ubq/118602/"
date_modified: "2026-08-04T08:11:45+00:00"
---

# A long, straight cylindrical conductor of radius \(R\) carries a uniform current density \(J\) directed parallel to its central axis. The conductor contains an off-axis cylindrical cavity of radius \(a\) running along its entire length, with central axis parallel to and displaced by a distance \(d\) from the main conductor’s central axis. Which of the following expressions correctly gives the magnitude of the magnetic field \(B\) at a point inside the cavity located at a distance \(r\) from the main conductor’s central axis?

A long, straight cylindrical conductor of radius \(R\) carries a uniform current density \(J\) directed parallel to its central axis. The conductor contains an off-axis cylindrical cavity of radius \(a\) running along its entire length, with central axis parallel to and displaced by a distance \(d\) from the main conductor's central axis. Which of the following expressions correctly gives the magnitude of the magnetic field \(B\) at a point inside the cavity located at a distance \(r\) from the main conductor's central axis?

![A circular cross-section of a large solid cylinder of radius \(R\) centered at point \(O\). Inside this circle, an off-axis smaller circle of radius \(a\) is drawn, centered at point \(C\). A straight dashed line segment connects point \(O\) to point \(C\) and is labeled \(d\). A point \(P\) is drawn inside the smaller circle. A dashed line segment extends from point \(O\) to point \(P\) and is labeled \(r\). Uniformly spaced small circles with dots inside them are distributed throughout the region between the outer circle and inner circle, representing current density \(J\) directed out of the page. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831104-xZzsHT.jpg)

- **A.** \(\dfrac{\mu_0 J r}{2}\)
- **B.** \(\dfrac{\mu_0 J d}{2}\)
- **C.** \(\dfrac{\mu_0 J (r - d)}{2}\)
- **D.** \(\dfrac{\mu_0 J (r^2 - a^2)}{2r}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118602/*