---
title: "A thin, solid conducting disk of radius \\(R\\) and uniform thickness \\(t_0\\) rotates at a constant angular speed \\(\\omega_0\\) about a perpendicular axis through its center. A uniform magnetic field of magnitude \\(B\\) is applied perpendicular to the plane of the disk over a small localized region centered at a distance \\(r_0\\) from the axis of rotation, generating eddy currents that exert a magnetic braking torque of magnitude \\(\\tau_0\\) on the disk. The disk is replaced by a second disk made of the same conducting material and radius \\(R\\) but with thickness \\(2t_0\\), and it is rotated at an angular speed \\(2\\omega_0\\) in the same magnetic field. What is the magnitude of the magnetic braking torque exerted on the second disk?"
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url: "https://nerd-notes.com/ubq/125010/"
date_modified: "2026-09-28T14:13:13+00:00"
---

# A thin, solid conducting disk of radius \(R\) and uniform thickness \(t_0\) rotates at a constant angular speed \(\omega_0\) about a perpendicular axis through its center. A uniform magnetic field of magnitude \(B\) is applied perpendicular to the plane of the disk over a small localized region centered at a distance \(r_0\) from the axis of rotation, generating eddy currents that exert a magnetic braking torque of magnitude \(\tau_0\) on the disk. The disk is replaced by a second disk made of the same conducting material and radius \(R\) but with thickness \(2t_0\), and it is rotated at an angular speed \(2\omega_0\) in the same magnetic field. What is the magnitude of the magnetic braking torque exerted on the second disk?

A thin, solid conducting disk of radius \(R\) and uniform thickness \(t_0\) rotates at a constant angular speed \(\omega_0\) about a perpendicular axis through its center. A uniform magnetic field of magnitude \(B\) is applied perpendicular to the plane of the disk over a small localized region centered at a distance \(r_0\) from the axis of rotation, generating eddy currents that exert a magnetic braking torque of magnitude \(\tau_0\) on the disk. The disk is replaced by a second disk made of the same conducting material and radius \(R\) but with thickness \(2t_0\), and it is rotated at an angular speed \(2\omega_0\) in the same magnetic field. What is the magnitude of the magnetic braking torque exerted on the second disk?

![A circular disk is viewed from above in a flat perspective. A central dot marks the rotation axis, with a curved counterclockwise arrow near the center labeled \(\omega_0\). A dashed radial reference line extends horizontally to the right from the center to the disk's outer edge, labeled \(R\). A small shaded circular patch represents the localized magnetic field region, centered on the horizontal line at a distance \(r_0\) from the central axis. Inside the small circular patch, exactly four small cross symbols indicate a magnetic field directed into the page, labeled \(B\). A straight dashed arrow tangent to the path of the patch points upward, indicating the local velocity. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604793-PRpLm5.jpg)

- **A.** \(2\tau_0\)
- **B.** \(4\tau_0\)
- **C.** \(8\tau_0\)
- **D.** \(16\tau_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125010/*