---
title: "A flat, stationary circular loop of wire of radius \\(a\\) is placed in a region of uniform magnetic field directed perpendicular to the plane of the loop. The magnitude of the magnetic field decreases exponentially with time according to \\(B(t) = B_0 e^{-t/\\tau}\\), where \\(B_0\\) and \\(\\tau\\) are positive constants. Which of the following expressions represents the magnitude of the induced electromotive force (EMF) in the loop at time \\(t = \\tau\\)?"
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url: "https://nerd-notes.com/ubq/118679/"
date_modified: "2026-08-04T08:13:41+00:00"
---

# A flat, stationary circular loop of wire of radius \(a\) is placed in a region of uniform magnetic field directed perpendicular to the plane of the loop. The magnitude of the magnetic field decreases exponentially with time according to \(B(t) = B_0 e^{-t/\tau}\), where \(B_0\) and \(\tau\) are positive constants. Which of the following expressions represents the magnitude of the induced electromotive force (EMF) in the loop at time \(t = \tau\)?

A flat, stationary circular loop of wire of radius \(a\) is placed in a region of uniform magnetic field directed perpendicular to the plane of the loop. The magnitude of the magnetic field decreases exponentially with time according to \(B(t) = B_0 e^{-t/\tau}\), where \(B_0\) and \(\tau\) are positive constants. Which of the following expressions represents the magnitude of the induced electromotive force (EMF) in the loop at time \(t = \tau\)?

![A flat circular loop of wire with radius a is centered at the origin of a horizontal plane, viewed at a 30-degree tilt from above. A thick dashed line extends along the central axis perpendicular to the loop plane, pointing vertically upward. Four parallel vertical arrows representing a uniform magnetic field \vec{B}(t) pass through the interior of the loop, all pointing upward. A radial dashed line drawn from the center of the loop to its perimeter is labeled a. Near the top of the field arrows, a label reads \vec{B}(t) = B_0 e^{-t/\tau}. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831220-Wbw4C0.jpg)

- **A.** \(\dfrac{\pi a^2 B_0}{\tau}\)
- **B.** \(\dfrac{\pi a^2 B_0}{e \tau}\)
- **C.** \(\dfrac{(e - 1)\pi a^2 B_0}{e \tau}\)
- **D.** \(\dfrac{\pi a^2 B_0}{e^2 \tau}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118679/*