---
title: "A flat circular loop of radius \\(R\\) carries a steady current \\(I\\). The loop is initially oriented in a uniform magnetic field \\(\\vec{B}\\) such that its magnetic dipole moment \\(\\vec{\\mu}\\) is aligned parallel to \\(\\vec{B}\\). An external agent slowly rotates the loop until its magnetic dipole moment makes an angle \\(\\theta\\) with \\(\\vec{B}\\). Which of the following expressions represents the work done by the external agent on the loop during this rotation?"
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url: "https://nerd-notes.com/ubq/118573/"
date_modified: "2026-08-04T08:11:24+00:00"
---

# A flat circular loop of radius \(R\) carries a steady current \(I\). The loop is initially oriented in a uniform magnetic field \(\vec{B}\) such that its magnetic dipole moment \(\vec{\mu}\) is aligned parallel to \(\vec{B}\). An external agent slowly rotates the loop until its magnetic dipole moment makes an angle \(\theta\) with \(\vec{B}\). Which of the following expressions represents the work done by the external agent on the loop during this rotation?

A flat circular loop of radius \(R\) carries a steady current \(I\). The loop is initially oriented in a uniform magnetic field \(\vec{B}\) such that its magnetic dipole moment \(\vec{\mu}\) is aligned parallel to \(\vec{B}\). An external agent slowly rotates the loop until its magnetic dipole moment makes an angle \(\theta\) with \(\vec{B}\). Which of the following expressions represents the work done by the external agent on the loop during this rotation?

![A diagram showing a circular loop of radius R carrying current I in a uniform magnetic field vector B. On the left, the loop lies in a vertical plane perpendicular to horizontal magnetic field lines directed to the right, labeled B. A magnetic dipole moment arrow labeled \mu points to the right, parallel to B. On the right, the same loop is shown rotated by an angle \theta about a vertical axis. The rotated dipole moment arrow \mu is tilted at angle \theta relative to the horizontal magnetic field lines. An arc with label \theta indicates the angle between \mu and B. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831084-xaM0rZ.jpg)

- **A.** \(I \pi R^2 B \sin\theta\)
- **B.** \(I \pi R^2 B \cos\theta\)
- **C.** \(I \pi R^2 B (1 + \cos\theta)\)
- **D.** \(I \pi R^2 B (1 - \cos\theta)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118573/*