---
title: "A rigid planar wire loop carrying a steady current is placed in a uniform magnetic field \\(\\vec{B}\\) and is free to rotate about a fixed axis perpendicular to the field lines. The orientation of the loop is described by the angle \\(\\theta\\) between its magnetic dipole moment \\(\\vec{\\mu}\\) and the magnetic field \\(\\vec{B}\\), over the full rotation from \\(\\theta = 0^\\circ\\) to \\(\\theta = 360^\\circ\\). Which of the following correctly describes the qualitative graph of the net magnetic torque \\(\\tau\\) exerted on the loop as a function of \\(\\theta\\), and correctly identifies the stability of the equilibrium at \\(\\theta = 180^\\circ\\)?"
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url: "https://nerd-notes.com/ubq/123238/"
date_modified: "2026-09-28T11:58:00+00:00"
---

# A rigid planar wire loop carrying a steady current is placed in a uniform magnetic field \(\vec{B}\) and is free to rotate about a fixed axis perpendicular to the field lines. The orientation of the loop is described by the angle \(\theta\) between its magnetic dipole moment \(\vec{\mu}\) and the magnetic field \(\vec{B}\), over the full rotation from \(\theta = 0^\circ\) to \(\theta = 360^\circ\). Which of the following correctly describes the qualitative graph of the net magnetic torque \(\tau\) exerted on the loop as a function of \(\theta\), and correctly identifies the stability of the equilibrium at \(\theta = 180^\circ\)?

A rigid planar wire loop carrying a steady current is placed in a uniform magnetic field \(\vec{B}\) and is free to rotate about a fixed axis perpendicular to the field lines. The orientation of the loop is described by the angle \(\theta\) between its magnetic dipole moment \(\vec{\mu}\) and the magnetic field \(\vec{B}\), over the full rotation from \(\theta = 0^\circ\) to \(\theta = 360^\circ\). Which of the following correctly describes the qualitative graph of the net magnetic torque \(\tau\) exerted on the loop as a function of \(\theta\), and correctly identifies the stability of the equilibrium at \(\theta = 180^\circ\)?

![A rectangular wire loop is tilted in three-dimensional perspective, centered on a vertical dashed line representing the rotation axis. Four horizontal, parallel, rightward-pointing solid arrows labeled \vec{B} represent a uniform magnetic field. A dashed normal arrow labeled \vec{\mu} extends outward perpendicular from the center of the loop face. An arc labeled \theta indicates the angle measured from the horizontal direction of \vec{B} to the normal vector \vec{\mu}. A small curved arrow along the wire indicates steady current I around the loop. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596680-cPIxH8.jpg)

- **A.** A cosine curve that reaches maximum magnitude at \(\theta = 0^\circ\) and \(\theta = 360^\circ\) and has zeros at \(\theta = 90^\circ\) and \(\theta = 270^\circ\); the equilibrium at \(\theta = 180^\circ\) is unstable.
- **B.** A sinusoidal curve that has zeros at \(\theta = 0^\circ\), \(\theta = 180^\circ\), and \(\theta = 360^\circ\) and reaches extrema at \(\theta = 90^\circ\) and \(\theta = 270^\circ\); the equilibrium at \(\theta = 180^\circ\) is unstable.
- **C.** A sinusoidal curve that has zeros at \(\theta = 0^\circ\), \(\theta = 180^\circ\), and \(\theta = 360^\circ\) and reaches extrema at \(\theta = 90^\circ\) and \(\theta = 270^\circ\); the equilibrium at \(\theta = 180^\circ\) is stable.
- **D.** A cosine curve that reaches maximum magnitude at \(\theta = 0^\circ\) and \(\theta = 360^\circ\) and has zeros at \(\theta = 90^\circ\) and \(\theta = 270^\circ\); the equilibrium at \(\theta = 180^\circ\) is stable.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123238/*