---
title: "A straight wire segment of length \\(L\\) lies in the \\(xy\\)-plane with one end anchored at the origin. The wire carries a constant electric current \\(I\\) and extends into the first quadrant, making an angle \\(\\theta\\) with the positive \\(x\\)-axis. A non-uniform magnetic field pointing in the \\(+z\\)-direction (out of the page) is present in the region, given by \\(\\vec{B}(x) = B_0 \\left(\\dfrac{x}{L}\\right) \\hat{k}\\), where \\(B_0\\) is a positive constant. What is the magnitude of the net magnetic force acting on the wire segment?"
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url: "https://nerd-notes.com/ubq/118538/"
date_modified: "2026-08-04T08:11:15+00:00"
---

# A straight wire segment of length \(L\) lies in the \(xy\)-plane with one end anchored at the origin. The wire carries a constant electric current \(I\) and extends into the first quadrant, making an angle \(\theta\) with the positive \(x\)-axis. A non-uniform magnetic field pointing in the \(+z\)-direction (out of the page) is present in the region, given by \(\vec{B}(x) = B_0 \left(\dfrac{x}{L}\right) \hat{k}\), where \(B_0\) is a positive constant. What is the magnitude of the net magnetic force acting on the wire segment?

A straight wire segment of length \(L\) lies in the \(xy\)-plane with one end anchored at the origin. The wire carries a constant electric current \(I\) and extends into the first quadrant, making an angle \(\theta\) with the positive \(x\)-axis. A non-uniform magnetic field pointing in the \(+z\)-direction (out of the page) is present in the region, given by \(\vec{B}(x) = B_0 \left(\dfrac{x}{L}\right) \hat{k}\), where \(B_0\) is a positive constant. What is the magnitude of the net magnetic force acting on the wire segment?

![A 2D schematic diagram in the xy-plane showing a straight wire segment of length L originating from the origin (0,0) and extending into the first quadrant at an angle \theta relative to the horizontal x-axis. An arrow labeled I points along the wire away from the origin to indicate current flow. A set of small circle-dot symbols representing a magnetic field \vec{B} pointing out of the page are distributed in the xy-plane, with higher density at larger x-values. The axes are labeled x and y, and a dashed arc indicates the angle \theta between the x-axis and the wire segment. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831074-dh2FFH.jpg)

- **A.** \(\dfrac{1}{2} I B_0 L \sin\theta\)
- **B.** \(I B_0 L \sin\theta\)
- **C.** \(I B_0 L \cos\theta\)
- **D.** \(\dfrac{1}{2} I B_0 L \cos\theta\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118538/*