---
title: "Three identical flat wire loops, each of area \\(A\\) and carrying a steady current \\(I\\), are placed in a region containing a uniform magnetic field \\(\\vec{B} = B_0 \\hat{i}\\). Loop 1 lies in the \\(yz\\)-plane, Loop 2 lies in the \\(xy\\)-plane, and Loop 3 lies in a plane whose unit normal vector is oriented at an angle of \\(45^\\circ\\) relative to the \\(+x\\)-axis. Which of the following correctly compares the magnitude of the net magnetic force \\(\\vec{F}_{\\text{net}}\\) and the magnitude of the net magnetic torque \\(\\tau_{\\text{net}}\\) exerted on each loop?"
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url: "https://nerd-notes.com/ubq/121274/"
date_modified: "2026-08-23T04:59:10+00:00"
---

# Three identical flat wire loops, each of area \(A\) and carrying a steady current \(I\), are placed in a region containing a uniform magnetic field \(\vec{B} = B_0 \hat{i}\). Loop 1 lies in the \(yz\)-plane, Loop 2 lies in the \(xy\)-plane, and Loop 3 lies in a plane whose unit normal vector is oriented at an angle of \(45^\circ\) relative to the \(+x\)-axis. Which of the following correctly compares the magnitude of the net magnetic force \(\vec{F}_{\text{net}}\) and the magnitude of the net magnetic torque \(\tau_{\text{net}}\) exerted on each loop?

Three identical flat wire loops, each of area \(A\) and carrying a steady current \(I\), are placed in a region containing a uniform magnetic field \(\vec{B} = B_0 \hat{i}\). Loop 1 lies in the \(yz\)-plane, Loop 2 lies in the \(xy\)-plane, and Loop 3 lies in a plane whose unit normal vector is oriented at an angle of \(45^\circ\) relative to the \(+x\)-axis. Which of the following correctly compares the magnitude of the net magnetic force \(\vec{F}_{\text{net}}\) and the magnitude of the net magnetic torque \(\tau_{\text{net}}\) exerted on each loop?

![A three-dimensional Cartesian coordinate system with three mutually perpendicular axes labeled x, y, and z. The x-axis extends horizontally to the right, the y-axis extends obliquely forward and to the left, and the z-axis extends vertically upward. Four parallel horizontal dashed arrows pointing to the right along the x-direction represent a uniform magnetic field labeled \vec{B}. Three identical circular loops of wire are shown: Loop 1 is positioned in the yz-plane centered at the origin, Loop 2 is positioned in the xy-plane, and Loop 3 is tilted such that its planar surface is angled at 45 degrees relative to the yz-plane. Each loop has an arrow along its perimeter indicating a counterclockwise current labeled I. Text labels 'Loop 1', 'Loop 2', and 'Loop 3' appear directly beside their respective loops. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461150-MlALrJ.jpg)

- **A.** | Net Force on Each Loop | Loop 1 Torque | Loop 2 Torque | Loop 3 Torque | | :---: | :---: | :---: | :---: | | Nonzero | \(I A B_0\) | \(0\) | \(\dfrac{\sqrt{2}}{2} I A B_0\) |
- **B.** | Net Force on Each Loop | Loop 1 Torque | Loop 2 Torque | Loop 3 Torque | | :---: | :---: | :---: | :---: | | \(0\) | \(I A B_0\) | \(0\) | \(\dfrac{\sqrt{2}}{2} I A B_0\) |
- **C.** | Net Force on Each Loop | Loop 1 Torque | Loop 2 Torque | Loop 3 Torque | | :---: | :---: | :---: | :---: | | \(0\) | \(0\) | \(I A B_0\) | \(\dfrac{\sqrt{2}}{2} I A B_0\) |
- **D.** | Net Force on Each Loop | Loop 1 Torque | Loop 2 Torque | Loop 3 Torque | | :---: | :---: | :---: | :---: | | \(0\) | \(0\) | \(0\) | \(0\) |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121274/*