---
title: "A planar rectangular coil with \\(N\\) tightly wound turns has a width \\(w\\) and a height \\(h\\), carrying a steady electric current \\(I\\). The coil is placed in a uniform horizontal magnetic field of magnitude \\(B\\) and is free to rotate about a fixed vertical axis that passes through the midpoints of its top and bottom horizontal segments of length \\(w\\). As viewed from above, the plane of the coil makes an angle \\(\\theta\\) with the direction of the magnetic field, where \\(0 \\le \\theta < \\dfrac{\\pi}{2}\\). Which of the following expressions represents the magnitude of the net magnetic torque exerted on the coil about the vertical rotation axis?"
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url: "https://nerd-notes.com/ubq/123227/"
date_modified: "2026-09-28T11:57:58+00:00"
---

# A planar rectangular coil with \(N\) tightly wound turns has a width \(w\) and a height \(h\), carrying a steady electric current \(I\). The coil is placed in a uniform horizontal magnetic field of magnitude \(B\) and is free to rotate about a fixed vertical axis that passes through the midpoints of its top and bottom horizontal segments of length \(w\). As viewed from above, the plane of the coil makes an angle \(\theta\) with the direction of the magnetic field, where \(0 \le \theta < \dfrac{\pi}{2}\). Which of the following expressions represents the magnitude of the net magnetic torque exerted on the coil about the vertical rotation axis?

A planar rectangular coil with \(N\) tightly wound turns has a width \(w\) and a height \(h\), carrying a steady electric current \(I\). The coil is placed in a uniform horizontal magnetic field of magnitude \(B\) and is free to rotate about a fixed vertical axis that passes through the midpoints of its top and bottom horizontal segments of length \(w\). As viewed from above, the plane of the coil makes an angle \(\theta\) with the direction of the magnetic field, where \(0 \le \theta < \dfrac{\pi}{2}\). Which of the following expressions represents the magnitude of the net magnetic torque exerted on the coil about the vertical rotation axis?

![A schematic top-down view showing a rectangular coil pivoted about a central vertical axis. Two horizontal parallel arrows pointing to the right represent a uniform magnetic field labeled B. A tilted solid line segment of length w represents the top edge of the coil, centered on a small filled circle representing the vertical rotation axis. A horizontal dashed reference line passes through the center dot parallel to B. An acute angle labeled \theta is indicated between the tilted segment and the horizontal dashed reference line. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596678-z3U6Nl.jpg)

- **A.** \(\dfrac{1}{2} N I w h B \sin\theta\)
- **B.** \(N I w h B \sin\theta\)
- **C.** \(N I w h B \cos\theta\)
- **D.** \(2 N I w h B \cos\theta\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123227/*