---
title: "A thin, circular wire loop of radius \\(R\\) lies in the \\(xy\\)-plane centered at the origin and carries a steady current \\(I\\) in the counterclockwise direction when viewed from the positive \\(z\\)-axis. The loop is placed in a uniform external magnetic field \\(\\vec{B}_0\\) that lies in the \\(xz\\)-plane and makes an angle \\(\\theta\\) with the positive \\(z\\)-axis, where \\(0 < \\theta < 90^\\circ\\). Which of the following expressions represents the magnitude of the net magnetic field at the center of the loop?"
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url: "https://nerd-notes.com/ubq/116409/"
date_modified: "2026-08-03T12:23:46+00:00"
---

# A thin, circular wire loop of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a steady current \(I\) in the counterclockwise direction when viewed from the positive \(z\)-axis. The loop is placed in a uniform external magnetic field \(\vec{B}_0\) that lies in the \(xz\)-plane and makes an angle \(\theta\) with the positive \(z\)-axis, where \(0 < \theta < 90^\circ\). Which of the following expressions represents the magnitude of the net magnetic field at the center of the loop?

A thin, circular wire loop of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a steady current \(I\) in the counterclockwise direction when viewed from the positive \(z\)-axis. The loop is placed in a uniform external magnetic field \(\vec{B}_0\) that lies in the \(xz\)-plane and makes an angle \(\theta\) with the positive \(z\)-axis, where \(0 < \theta < 90^\circ\). Which of the following expressions represents the magnitude of the net magnetic field at the center of the loop?

![A 3D coordinate system with axes labeled x, y, and z. A flat circular loop of radius R lies in the xy-plane, centered at the origin. Arrows along the loop indicate counterclockwise current I when viewed from above looking down along the z-axis. A uniform external magnetic field vector labeled B_0 starts at the origin and points into the xz-plane at an angle theta measured relative to the positive z-axis. Dashed projection lines show the components of B_0 along the x-axis and z-axis. No other text, lines, or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785759826-W4Qto2.jpg)

- **A.** \(\sqrt{B_0^2 + \left(\dfrac{\mu_0 I}{2R}\right)^2 + \dfrac{\mu_0 I B_0 \sin\theta}{R}}\)
- **B.** \(\sqrt{B_0^2 + \left(\dfrac{\mu_0 I}{2\pi R}\right)^2 + \dfrac{\mu_0 I B_0 \cos\theta}{\pi R}}\)
- **C.** \(\sqrt{B_0^2 + \left(\dfrac{\mu_0 I}{2R}\right)^2 + \dfrac{\mu_0 I B_0 \cos\theta}{R}}\)
- **D.** \(B_0 + \dfrac{\mu_0 I}{2R} \cos\theta\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116409/*