---
title: "Three long, straight, parallel wires labeled Wire 1, Wire 2, and Wire 3 lie in the xy-plane and carry equal currents \\(I\\) directed out of the page in the \\(+z\\)-direction. Wire 1 is fixed at \\(x = 0\\), Wire 2 is fixed at \\(x = d\\), and Wire 3 is fixed at \\(x = 3d\\). Which of the following correctly pairs the ratio of the magnitude of the net magnetic force per unit length on Wire 1 to that on Wire 3, \\(F_1 / F_3\\), with the magnitude of the net magnetic field at the midpoint between Wire 1 and Wire 2?"
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url: "https://nerd-notes.com/ubq/118628/"
date_modified: "2026-08-04T08:12:24+00:00"
---

# Three long, straight, parallel wires labeled Wire 1, Wire 2, and Wire 3 lie in the xy-plane and carry equal currents \(I\) directed out of the page in the \(+z\)-direction. Wire 1 is fixed at \(x = 0\), Wire 2 is fixed at \(x = d\), and Wire 3 is fixed at \(x = 3d\). Which of the following correctly pairs the ratio of the magnitude of the net magnetic force per unit length on Wire 1 to that on Wire 3, \(F_1 / F_3\), with the magnitude of the net magnetic field at the midpoint between Wire 1 and Wire 2?

Three long, straight, parallel wires labeled Wire 1, Wire 2, and Wire 3 lie in the xy-plane and carry equal currents \(I\) directed out of the page in the \(+z\)-direction. Wire 1 is fixed at \(x = 0\), Wire 2 is fixed at \(x = d\), and Wire 3 is fixed at \(x = 3d\). Which of the following correctly pairs the ratio of the magnitude of the net magnetic force per unit length on Wire 1 to that on Wire 3, \(F_1 / F_3\), with the magnitude of the net magnetic field at the midpoint between Wire 1 and Wire 2?

![A Cartesian coordinate system in the xy-plane showing three circular cross-sections of thin parallel wires perpendicular to the plane. Wire 1 is centered on the y-axis at x = 0, Wire 2 is centered at x = d, and Wire 3 is centered at x = 3d. Each wire cross-section is drawn as a small circle with a solid black dot in its center, indicating current out of the page labeled I. A horizontal x-axis extends through the centers of all three wires, labeled with tick marks at x = 0, x = d, x = 3d, and a tick mark at x = d/2 labeled with a point P. Dimension arrows beneath the x-axis show a distance d between Wire 1 and Wire 2, and a distance 2d between Wire 2 and Wire 3. A vertical y-axis extends upward from x = 0. No other labels, arrows, vectors, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831143-7KrcwB.jpg)

- **A.** Ratio \(F_1 / F_3 = \dfrac{5}{8}\), Field magnitude \(B_{\text{net}} = \dfrac{\mu_0 I}{5\pi d}\)
- **B.** Ratio \(F_1 / F_3 = 2\), Field magnitude \(B_{\text{net}} = 0\)
- **C.** Ratio \(F_1 / F_3 = \dfrac{8}{5}\), Field magnitude \(B_{\text{net}} = \dfrac{\mu_0 I}{5\pi d}\)
- **D.** Ratio \(F_1 / F_3 = \dfrac{8}{5}\), Field magnitude \(B_{\text{net}} = \dfrac{11\mu_0 I}{5\pi d}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118628/*