---
title: "A long, straight wire carries a constant current \\(I\\). A rectangular loop with side lengths \\(L\\) parallel to the wire and \\(w\\) perpendicular to the wire lies in the plane of the wire, with its nearest edge at a distance \\(d\\) from the wire. Which of the following expressions represents the total magnetic flux \\(\\Phi_B\\) through the loop?"
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url: "https://nerd-notes.com/ubq/118647/"
date_modified: "2026-08-04T08:13:29+00:00"
---

# A long, straight wire carries a constant current \(I\). A rectangular loop with side lengths \(L\) parallel to the wire and \(w\) perpendicular to the wire lies in the plane of the wire, with its nearest edge at a distance \(d\) from the wire. Which of the following expressions represents the total magnetic flux \(\Phi_B\) through the loop?

A long, straight wire carries a constant current \(I\). A rectangular loop with side lengths \(L\) parallel to the wire and \(w\) perpendicular to the wire lies in the plane of the wire, with its nearest edge at a distance \(d\) from the wire. Which of the following expressions represents the total magnetic flux \(\Phi_B\) through the loop?

![A long vertical wire on the left carries a current labeled I pointing upward. To the right of the wire lies a rectangular loop in the same plane. The vertical sides of the loop have length L, parallel to the long wire. The horizontal sides have width w, perpendicular to the wire. A horizontal dashed line segment indicates the distance d from the long wire to the left vertical edge of the rectangular loop. The width of the loop is labeled w along the bottom horizontal side, and the height of the loop is labeled L along the right vertical side. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831209-mkB2bH.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118647/*