---
title: "A long, solid cylindrical conductor of radius \\(R\\) carries a uniform current density \\(J\\) parallel to its central axis. A cylindrical cavity of radius \\(a\\) is drilled parallel to the conductor’s axis, with its center displaced by a distance \\(d\\) from the central axis of the conductor, where \\(d + a < R\\). Which of the following expressions represents the magnitude of the magnetic field at any point inside the cavity?"
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url: "https://nerd-notes.com/ubq/118531/"
date_modified: "2026-08-04T08:11:14+00:00"
---

# A long, solid cylindrical conductor of radius \(R\) carries a uniform current density \(J\) parallel to its central axis. A cylindrical cavity of radius \(a\) is drilled parallel to the conductor’s axis, with its center displaced by a distance \(d\) from the central axis of the conductor, where \(d + a < R\). Which of the following expressions represents the magnitude of the magnetic field at any point inside the cavity?

A long, solid cylindrical conductor of radius \(R\) carries a uniform current density \(J\) parallel to its central axis. A cylindrical cavity of radius \(a\) is drilled parallel to the conductor's axis, with its center displaced by a distance \(d\) from the central axis of the conductor, where \(d + a < R\). Which of the following expressions represents the magnitude of the magnetic field at any point inside the cavity?

![Cross-sectional view of a large outer circle of radius R centered at point O. Inside the large circle, a smaller circle of radius a is centered at point O', displaced to the right along a horizontal dashed line by a distance d from O. A position vector r points from O to an arbitrary point P inside the smaller circle. Current density vectors J are indicated pointing out of the page throughout the region between the inner and outer circles. No other lines, labels, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831074-GbxxZU.jpg)

- **A.** \(\mu_0 J r\)
- **B.** \(\dfrac{1}{2}\mu_0 J d\)
- **C.** \(\dfrac{1}{2}\mu_0 J \dfrac{a^2}{d}\)
- **D.** \(\dfrac{1}{2}\mu_0 J (R - d)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118531/*