---
title: "A long, thick cylindrical conducting tube of inner radius \\(a\\) and outer radius \\(b\\) carries a uniformly distributed total current \\(I\\) parallel to its central axis. Which of the following correctly states the magnitude of the magnetic field \\(B\\) in the hollow central cavity (\\(r < a\\)) and inside the wall of the tube (\\(a < r < b\\)), along with the correct physical justification?"
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url: "https://nerd-notes.com/ubq/118533/"
date_modified: "2026-08-04T08:11:14+00:00"
---

# A long, thick cylindrical conducting tube of inner radius \(a\) and outer radius \(b\) carries a uniformly distributed total current \(I\) parallel to its central axis. Which of the following correctly states the magnitude of the magnetic field \(B\) in the hollow central cavity (\(r < a\)) and inside the wall of the tube (\(a < r < b\)), along with the correct physical justification?

A long, thick cylindrical conducting tube of inner radius \(a\) and outer radius \(b\) carries a uniformly distributed total current \(I\) parallel to its central axis. Which of the following correctly states the magnitude of the magnetic field \(B\) in the hollow central cavity (\(r < a\)) and inside the wall of the tube (\(a < r < b\)), along with the correct physical justification?

![A cross-sectional view of a thick cylindrical shell centered at the origin. An inner circle of radius \(a\) bounds a hollow central cavity centered at the origin, shown in white. An outer circle of radius \(b\) bounds the conductor wall, shaded light gray between radius \(a\) and radius \(b\). Small dots with circles around them are distributed evenly throughout the light gray shaded region to indicate current flowing uniformly out of the page, labeled \(I\). A radial dashed line from the center to the inner boundary is labeled \(a\). A radial dashed line from the center to the outer boundary is labeled \(b\). A point in the central cavity at distance \(r < a\) from the center is labeled \(P_1\). A point in the conductor wall at distance \(a < r < b\) from the center is labeled \(P_2\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831074-wyZcj6.jpg)

- **A.** The magnetic field is non-zero in the cavity (\(r < a\)) because magnetic field lines produced by the current in the outer wall penetrate into the interior, and zero in the wall (\(a < r < b\)) because the current density is uniform.
- **B.** The magnetic field is zero in both the cavity (\(r < a\)) and the wall (\(a < r < b\)) because magnetic fields cannot exist inside a conductor in magnetostatic equilibrium.
- **C.** The magnetic field is zero in the cavity (\(r < a\)) because charge carriers only flow on the inner surface \(r = a\), and non-zero in the wall (\(a < r < b\)) because an Amperian loop encloses all of the current \(I\) for any radius \(r > a\).
- **D.** The magnetic field is zero in the cavity (\(r < a\)) because a concentric circular Amperian loop encloses zero current, and non-zero in the wall (\(a < r < b\)) because a concentric circular Amperian loop encloses a non-zero fraction of the total current.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118533/*