---
title: "A long, solid cylindrical conductor carries a uniform current density \\(J\\) directed parallel to its central axis. A cylindrical cavity is drilled through the conductor parallel to the central axis, with its center displaced by a distance \\(d\\) from the conductor’s axis. At a location inside the cavity situated at a distance \\(r\\) from the central axis of the conductor, which of the following gives the magnitude of the magnetic field?"
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url: "https://nerd-notes.com/ubq/121230/"
date_modified: "2026-08-23T04:58:57+00:00"
---

# A long, solid cylindrical conductor carries a uniform current density \(J\) directed parallel to its central axis. A cylindrical cavity is drilled through the conductor parallel to the central axis, with its center displaced by a distance \(d\) from the conductor’s axis. At a location inside the cavity situated at a distance \(r\) from the central axis of the conductor, which of the following gives the magnitude of the magnetic field?

A long, solid cylindrical conductor carries a uniform current density \(J\) directed parallel to its central axis. A cylindrical cavity is drilled through the conductor parallel to the central axis, with its center displaced by a distance \(d\) from the conductor's axis. At a location inside the cavity situated at a distance \(r\) from the central axis of the conductor, which of the following gives the magnitude of the magnetic field?

![A circular cross section of a large solid cylinder centered at a point labeled O_1. Inside the large circle, an off-center smaller circular region represents a cavity centered at point O_2. A dashed straight line segment connects O_1 to O_2, accompanied by a dimension label d indicating the center-to-center distance. A point labeled P is located inside the smaller circle, with a dashed line extending from O_1 to P labeled r. An out-of-page circle-dot symbol labeled \vec{J} is positioned in the shaded conducting region between the outer boundary and the cavity. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461137-Sho0fv.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121230/*