---
title: "A small magnetic dipole with dipole moment \\(\\vec{\\mu}\\) is located at the center of a fixed, flat circular conducting loop lying in the \\(xy\\)-plane. Initially at time \\(t = 0\\), \\(\\vec{\\mu}\\) points in the \\(+z\\)-direction. The dipole is then forced to rotate at a constant angular speed \\(\\omega\\) about the \\(x\\)-axis toward the \\(+y\\)-axis, such that its orientation is given by \\(\\vec{\\mu}(t) = \\mu \\cos(\\omega t)\\hat{k} + \\mu \\sin(\\omega t)\\hat{j}\\). Which of the following correctly identifies the direction of the magnetic field \\(\\vec{B}_{\\text{ring}}\\) produced at the origin by the induced current in the loop, and the direction of the magnetic torque \\(\\vec{\\tau}\\) exerted on the dipole by \\(\\vec{B}_{\\text{ring}}\\), at the instant \\(\\omega t = \\dfrac{\\pi}{2}\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118703/"
date_modified: "2026-08-04T08:13:48+00:00"
---

# A small magnetic dipole with dipole moment \(\vec{\mu}\) is located at the center of a fixed, flat circular conducting loop lying in the \(xy\)-plane. Initially at time \(t = 0\), \(\vec{\mu}\) points in the \(+z\)-direction. The dipole is then forced to rotate at a constant angular speed \(\omega\) about the \(x\)-axis toward the \(+y\)-axis, such that its orientation is given by \(\vec{\mu}(t) = \mu \cos(\omega t)\hat{k} + \mu \sin(\omega t)\hat{j}\). Which of the following correctly identifies the direction of the magnetic field \(\vec{B}_{\text{ring}}\) produced at the origin by the induced current in the loop, and the direction of the magnetic torque \(\vec{\tau}\) exerted on the dipole by \(\vec{B}_{\text{ring}}\), at the instant \(\omega t = \dfrac{\pi}{2}\)?

A small magnetic dipole with dipole moment \(\vec{\mu}\) is located at the center of a fixed, flat circular conducting loop lying in the \(xy\)-plane. Initially at time \(t = 0\), \(\vec{\mu}\) points in the \(+z\)-direction. The dipole is then forced to rotate at a constant angular speed \(\omega\) about the \(x\)-axis toward the \(+y\)-axis, such that its orientation is given by \(\vec{\mu}(t) = \mu \cos(\omega t)\hat{k} + \mu \sin(\omega t)\hat{j}\). Which of the following correctly identifies the direction of the magnetic field \(\vec{B}_{\text{ring}}\) produced at the origin by the induced current in the loop, and the direction of the magnetic torque \(\vec{\tau}\) exerted on the dipole by \(\vec{B}_{\text{ring}}\), at the instant \(\omega t = \dfrac{\pi}{2}\)?

![A three-dimensional Cartesian coordinate system with axes labeled x, y, and z. A thin, flat circular conducting loop lies in the xy-plane, centered at the origin. At the origin, a vector labeled \vec{\mu} lies in the yz-plane, tilted at an angle \theta from the z-axis toward the y-axis. A curved arrow around the x-axis indicates rotation of the dipole moment vector \vec{\mu} from the +z-axis toward the +y-axis. No other labels or vectors appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831228-i1PdAP.jpg)

- **A.** \(\vec{B}_{\text{ring}}\): \(-z\)-direction; \quad \vec{\tau}\): \(-x\)-direction
- **B.** \(\vec{B}_{\text{ring}}\): \(-z\)-direction; \quad \vec{\tau}\): \(+x\)-direction
- **C.** \(\vec{B}_{\text{ring}}\): \(+z\)-direction; \quad \vec{\tau}\): \(-x\)-direction
- **D.** \(\vec{B}_{\text{ring}}\): \(+z\)-direction; \quad \vec{\tau}\): \(+x\)-direction

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118703/*