---
title: "Three long, straight, parallel wires lie in the same plane as shown. Wire 1 is fixed at position \\(x = 0\\) carrying current \\(I_0\\) directed out of the page, and Wire 3 is fixed at position \\(x = d\\) carrying current \\(4I_0\\) directed out of the page. Wire 2 carries current \\(I_2\\) directed into the page and is placed between Wire 1 and Wire 3 at an equilibrium position \\(x\\) where the net magnetic force on Wire 2 is zero. In terms of \\(d\\), what is the equilibrium position \\(x\\) of Wire 2, and what is the direction of the net magnetic force on Wire 2 if it is displaced slightly toward Wire 3?"
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url: "https://nerd-notes.com/ubq/123442/"
date_modified: "2026-09-28T11:58:37+00:00"
---

# Three long, straight, parallel wires lie in the same plane as shown. Wire 1 is fixed at position \(x = 0\) carrying current \(I_0\) directed out of the page, and Wire 3 is fixed at position \(x = d\) carrying current \(4I_0\) directed out of the page. Wire 2 carries current \(I_2\) directed into the page and is placed between Wire 1 and Wire 3 at an equilibrium position \(x\) where the net magnetic force on Wire 2 is zero. In terms of \(d\), what is the equilibrium position \(x\) of Wire 2, and what is the direction of the net magnetic force on Wire 2 if it is displaced slightly toward Wire 3?

Three long, straight, parallel wires lie in the same plane as shown. Wire 1 is fixed at position \(x = 0\) carrying current \(I_0\) directed out of the page, and Wire 3 is fixed at position \(x = d\) carrying current \(4I_0\) directed out of the page. Wire 2 carries current \(I_2\) directed into the page and is placed between Wire 1 and Wire 3 at an equilibrium position \(x\) where the net magnetic force on Wire 2 is zero. In terms of \(d\), what is the equilibrium position \(x\) of Wire 2, and what is the direction of the net magnetic force on Wire 2 if it is displaced slightly toward Wire 3?

![A horizontal dashed axis labeled x with an arrowhead pointing to the right. Three circular wire cross-sections lie along the axis. On the left at x = 0 is a circle labeled Wire 1 containing a solid dot, with current label I_0. On the right at distance d is a circle labeled Wire 3 containing a solid dot, with current label 4I_0. Between them at distance x from Wire 1 is a circle labeled Wire 2 containing an X, with current label I_2. A horizontal dimension line with arrows spans from Wire 1 to Wire 2 labeled x. A second horizontal dimension line with arrows spans from Wire 1 to Wire 3 labeled d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596717-RXbUiS.jpg)

- **A.** \(x = \dfrac{d}{3}\); directed toward Wire 3
- **B.** \(x = \dfrac{d}{3}\); directed toward Wire 1
- **C.** \(x = \dfrac{d}{5}\); directed toward Wire 3
- **D.** \(x = \dfrac{d}{5}\); directed toward Wire 1

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123442/*