---
title: "A rectangular loop of wire with width \\(w\\) and length \\(L\\) carries a steady current \\(I\\) in a uniform magnetic field of magnitude \\(B\\). The loop is free to rotate about a central axis parallel to its length \\(L\\). The angle \\(\\phi\\) is defined as the angle between the plane of the loop and the magnetic field vector \\(\\vec{B}\\). Which of the following graphs best represents the net magnetic torque \\(\\tau\\) exerted on the loop as a function of \\(\\phi\\) from \\(\\phi = 0\\) to \\(\\phi = \\pi \\text{ rad}\\)?"
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url: "https://nerd-notes.com/ubq/117464/"
date_modified: "2026-08-04T06:52:14+00:00"
---

# A rectangular loop of wire with width \(w\) and length \(L\) carries a steady current \(I\) in a uniform magnetic field of magnitude \(B\). The loop is free to rotate about a central axis parallel to its length \(L\). The angle \(\phi\) is defined as the angle between the plane of the loop and the magnetic field vector \(\vec{B}\). Which of the following graphs best represents the net magnetic torque \(\tau\) exerted on the loop as a function of \(\phi\) from \(\phi = 0\) to \(\phi = \pi \text{ rad}\)?

A rectangular loop of wire with width \(w\) and length \(L\) carries a steady current \(I\) in a uniform magnetic field of magnitude \(B\). The loop is free to rotate about a central axis parallel to its length \(L\). The angle \(\phi\) is defined as the angle between the plane of the loop and the magnetic field vector \(\vec{B}\). Which of the following graphs best represents the net magnetic torque \(\tau\) exerted on the loop as a function of \(\phi\) from \(\phi = 0\) to \(\phi = \pi \text{ rad}\)?

![A 3D perspective schematic showing a rectangular wire loop of width w and length L situated in a uniform magnetic field B directed along the positive x-axis. The loop is tilted such that the angle between the plane of the loop and the magnetic field vectors is labeled \phi. An arrow indicates a steady counterclockwise current I flowing through the loop. The rotation axis passes lengthwise through the center of the loop, parallel to the sides of length L. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826334-81GHsH.jpg)

- **A.** A sinusoidal graph that starts at zero at \(\phi = 0\), reaches a maximum value of \(I w L B\) at \(\phi = \pi/2 \text{ rad}\), and returns to zero at \(\phi = \pi \text{ rad}\).
- **B.** A sinusoidal graph that starts at a maximum positive value of \(I w L B\) at \(\phi = 0\), decreases smoothly to zero at \(\phi = \pi/2 \text{ rad}\), and reaches a negative peak of \(-I w L B\) at \(\phi = \pi \text{ rad}\).
- **C.** A linear graph that decreases steadily from a maximum positive value of \(I w L B\) at \(\phi = 0\) to zero at \(\phi = \pi/2 \text{ rad}\), and continues linearly to \(-I w L B\) at \(\phi = \pi \text{ rad}\).
- **D.** A constant horizontal line at a value of \(I w L B\) for all angles from \(\phi = 0\) to \(\phi = \pi \text{ rad}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117464/*