---
title: "A flexible circular loop of wire with radius \\(r\\) and total resistance \\(R\\) lies in a plane perpendicular to a uniform magnetic field of magnitude \\(B\\). Over a time interval \\(\\Delta t\\), the loop is pulled symmetrically at four points and deformed into a square while maintaining a constant total length of wire. What is the magnitude of the average induced current in the loop during this time interval?"
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url: "https://nerd-notes.com/ubq/118669/"
date_modified: "2026-08-04T08:13:37+00:00"
---

# A flexible circular loop of wire with radius \(r\) and total resistance \(R\) lies in a plane perpendicular to a uniform magnetic field of magnitude \(B\). Over a time interval \(\Delta t\), the loop is pulled symmetrically at four points and deformed into a square while maintaining a constant total length of wire. What is the magnitude of the average induced current in the loop during this time interval?

A flexible circular loop of wire with radius \(r\) and total resistance \(R\) lies in a plane perpendicular to a uniform magnetic field of magnitude \(B\). Over a time interval \(\Delta t\), the loop is pulled symmetrically at four points and deformed into a square while maintaining a constant total length of wire. What is the magnitude of the average induced current in the loop during this time interval?

![Two side-by-side diagrams showing a wire loop in a magnetic field directed into the page. The magnetic field is represented by a 3 by 3 grid of small x symbols in each diagram. On the left, labeled Initial, a thin continuous circular loop of radius r is centered in the field. An arrow labeled r extends from the center of the circle to its top edge. On the right, labeled Final, the same wire is shown deformed into a square loop of side length s, with its sides parallel and perpendicular to the page edges. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831217-61KcsA.jpg)

- **A.** \(\dfrac{\pi r^2 B}{R \Delta t}\)
- **B.** \(\dfrac{\pi r^2 B}{R \Delta t} \left(1 - \dfrac{\pi}{4}\right)\)
- **C.** \(\dfrac{\pi r^2 B}{R \Delta t} \left(1 - \dfrac{1}{4}\right)\)
- **D.** \(\dfrac{\pi r^2 B}{R \Delta t} \left(1 - \dfrac{\pi}{2}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118669/*