---
title: "A long, straight wire carrying a current \\(I\\) lies in the plane of a square conducting loop of side length \\(a\\). The side of the loop nearest to the wire is parallel to the wire and separated from it by a distance \\(d\\). In terms of \\(a\\), \\(d\\), and fundamental constants, what is the mutual inductance \\(M\\) of the wire and loop system?"
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url: "https://nerd-notes.com/ubq/118650/"
date_modified: "2026-08-04T08:13:30+00:00"
---

# A long, straight wire carrying a current \(I\) lies in the plane of a square conducting loop of side length \(a\). The side of the loop nearest to the wire is parallel to the wire and separated from it by a distance \(d\). In terms of \(a\), \(d\), and fundamental constants, what is the mutual inductance \(M\) of the wire and loop system?

A long, straight wire carrying a current \(I\) lies in the plane of a square conducting loop of side length \(a\). The side of the loop nearest to the wire is parallel to the wire and separated from it by a distance \(d\). In terms of \(a\), \(d\), and fundamental constants, what is the mutual inductance \(M\) of the wire and loop system?

![A vertical long straight line representing a wire carrying current I upward, indicated by an arrow labeled I. To the right of the wire lies a coplanar square loop of side length a. The left edge of the square loop is parallel to the wire at a distance d, marked by a horizontal dimension line labeled d between the wire and the left edge. The top edge of the square loop is labeled a. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831210-MuxCTP.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118650/*