---
title: "A planar loop of wire with total electrical resistance \\(R\\) and area \\(A\\) rotates at a constant angular speed \\(\\omega\\) in a region of uniform, constant magnetic field \\(\\vec{B}\\). The rotation axis lies in the plane of the loop and is perpendicular to the magnetic field. If the angular speed of the loop is increased from an initial value \\(\\omega_0\\) to \\(2\\omega_0\\), by what factor does the total thermal energy dissipated in the loop during one complete revolution change?"
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url: "https://nerd-notes.com/ubq/124792/"
date_modified: "2026-09-28T14:11:18+00:00"
---

# A planar loop of wire with total electrical resistance \(R\) and area \(A\) rotates at a constant angular speed \(\omega\) in a region of uniform, constant magnetic field \(\vec{B}\). The rotation axis lies in the plane of the loop and is perpendicular to the magnetic field. If the angular speed of the loop is increased from an initial value \(\omega_0\) to \(2\omega_0\), by what factor does the total thermal energy dissipated in the loop during one complete revolution change?

A planar loop of wire with total electrical resistance \(R\) and area \(A\) rotates at a constant angular speed \(\omega\) in a region of uniform, constant magnetic field \(\vec{B}\). The rotation axis lies in the plane of the loop and is perpendicular to the magnetic field. If the angular speed of the loop is increased from an initial value \(\omega_0\) to \(2\omega_0\), by what factor does the total thermal energy dissipated in the loop during one complete revolution change?

![A perspective view showing a vertical dashed line representing the axis of rotation. A flat rectangular wire loop is centered on this axis, with the axis lying in the plane of the loop. A curved arrow at the top of the axis indicates rotation with angular speed \(\omega\). Five horizontal, parallel arrows pointing to the right indicate the uniform magnetic field \(\vec{B}\), which is perpendicular to the rotation axis. The wire loop is labeled with resistance \(R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604678-oY8yCe.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124792/*