---
title: "A flat rectangular loop of wire with area \\(A\\) rotates at a constant angular frequency \\(\\omega\\) about an axis in its plane inside a uniform, constant magnetic field \\(\\vec{B}\\). Which option correctly describes the time dependence of the induced electromotive force (EMF) in the loop, and the factor by which the peak induced EMF changes if the rotational speed is doubled to \\(2\\omega\\)?"
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url: "https://nerd-notes.com/ubq/118660/"
date_modified: "2026-08-04T08:13:35+00:00"
---

# A flat rectangular loop of wire with area \(A\) rotates at a constant angular frequency \(\omega\) about an axis in its plane inside a uniform, constant magnetic field \(\vec{B}\). Which option correctly describes the time dependence of the induced electromotive force (EMF) in the loop, and the factor by which the peak induced EMF changes if the rotational speed is doubled to \(2\omega\)?

A flat rectangular loop of wire with area \(A\) rotates at a constant angular frequency \(\omega\) about an axis in its plane inside a uniform, constant magnetic field \(\vec{B}\). Which option correctly describes the time dependence of the induced electromotive force (EMF) in the loop, and the factor by which the peak induced EMF changes if the rotational speed is doubled to \(2\omega\)?

![A rectangular wire loop is positioned between two magnetic poles, with the North pole on the left and the South pole on the right. Horizontal magnetic field vectors labeled \(\vec{B}\) point from left to right across the loop. A vertical dashed line passes through the center of the loop, representing the axis of rotation, with a curved arrow labeled \(\omega\) indicating rotational motion around this vertical axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831214-Fr7uO6.jpg)

- **A.** Time dependence: Sinusoidal | Peak EMF factor: 2
- **B.** Time dependence: Sinusoidal | Peak EMF factor: 4
- **C.** Time dependence: Constant | Peak EMF factor: 2
- **D.** Time dependence: Constant | Peak EMF factor: 4

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118660/*