---
title: "A long straight wire carrying a steady current \\(I_1\\) lies in the plane of a rigid rectangular wire loop carrying a steady current \\(I_2\\). Two sides of the rectangular loop, each of length \\(a\\), are parallel to the long wire, and the other two sides, each of length \\(b\\), are perpendicular to it. The side of length \\(a\\) closest to the long wire is located a distance \\(d\\) away, as shown in the diagram. What is the magnitude of the net magnetic force exerted on the rectangular loop by the field of the long wire?"
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url: "https://nerd-notes.com/ubq/118616/"
date_modified: "2026-08-04T08:11:53+00:00"
---

# A long straight wire carrying a steady current \(I_1\) lies in the plane of a rigid rectangular wire loop carrying a steady current \(I_2\). Two sides of the rectangular loop, each of length \(a\), are parallel to the long wire, and the other two sides, each of length \(b\), are perpendicular to it. The side of length \(a\) closest to the long wire is located a distance \(d\) away, as shown in the diagram. What is the magnitude of the net magnetic force exerted on the rectangular loop by the field of the long wire?

A long straight wire carrying a steady current \(I_1\) lies in the plane of a rigid rectangular wire loop carrying a steady current \(I_2\). Two sides of the rectangular loop, each of length \(a\), are parallel to the long wire, and the other two sides, each of length \(b\), are perpendicular to it. The side of length \(a\) closest to the long wire is located a distance \(d\) away, as shown in the diagram. What is the magnitude of the net magnetic force exerted on the rectangular loop by the field of the long wire?

![A 2D schematic diagram in the xy-plane showing a long straight vertical line labeled with an arrow pointing upward carrying current \(I_1\). To the right of the vertical line, a rectangular loop of wire is drawn with solid lines. The rectangular loop has two vertical sides of length \(a\) and two horizontal sides of length \(b\). The left vertical side of the loop is parallel to the long wire and separated from it by a horizontal dashed dimension line labeled \(d\). The horizontal top and bottom sides of the loop have length labeled \(b\), extending from \(x = d\) to \(x = d+b\). The vertical sides have length labeled \(a\). A clockwise arrow on the rectangular loop indicates a current \(I_2\). A small arrow pointing upward along the left side of the loop shows the direction of \(I_2\) on that segment. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831112-urC6fd.jpg)

- **A.** \(\dfrac{\mu_0 I_1 I_2 a}{2\pi d}\)
- **B.** \(\dfrac{\mu_0 I_1 I_2 a b}{2\pi d^2}\)
- **C.** \(\dfrac{\mu_0 I_1 I_2 a b}{2\pi d (d+b)}\)
- **D.** \(\dfrac{\mu_0 I_1 I_2}{2\pi} \ln\left(1 + \dfrac{b}{d}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118616/*