---
title: "A long, straight wire carries a constant current \\(I\\). A single-turn flat rectangular loop with length \\(L\\) parallel to the wire and width \\(w\\) perpendicular to the wire lies in the plane of the wire, with its nearest edge located a distance \\(d\\) from the wire. Which of the following integral expressions correctly gives the total magnetic flux \\(\\Phi_B\\) through the loop?"
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url: "https://nerd-notes.com/ubq/121289/"
date_modified: "2026-08-23T04:59:34+00:00"
---

# A long, straight wire carries a constant current \(I\). A single-turn flat rectangular loop with length \(L\) parallel to the wire and width \(w\) perpendicular to the wire lies in the plane of the wire, with its nearest edge located a distance \(d\) from the wire. Which of the following integral expressions correctly gives the total magnetic flux \(\Phi_B\) through the loop?

A long, straight wire carries a constant current \(I\). A single-turn flat rectangular loop with length \(L\) parallel to the wire and width \(w\) perpendicular to the wire lies in the plane of the wire, with its nearest edge located a distance \(d\) from the wire. Which of the following integral expressions correctly gives the total magnetic flux \(\Phi_B\) through the loop?

![A vertical solid line representing a long straight wire carries a current labeled I directed upward with an arrow on the wire. To the right of the wire, in the same plane, is a flat rectangular loop of height L and horizontal width w. The left edge of the rectangle is parallel to the wire and positioned at a horizontal distance d from the wire. A double-headed horizontal dimension arrow labeled d spans from the wire to the left edge of the loop. A double-headed horizontal dimension arrow labeled w spans the width of the loop from its left edge to its right edge. A double-headed vertical dimension arrow labeled L spans the height of the loop along its right edge. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461173-IsKqLn.jpg)

- **A.** \(\dfrac{\mu_0 I L}{2\pi} \int_{d}^{w} \dfrac{1}{r}\,dr\)
- **B.** \(\dfrac{\mu_0 I L}{2\pi} \int_{d}^{d+w} \dfrac{1}{r}\,dr\)
- **C.** \(\dfrac{\mu_0 I w}{2\pi} \int_{d}^{d+w} \dfrac{1}{r}\,dr\)
- **D.** \(\dfrac{\mu_0 I L}{2\pi} \int_{d}^{d+w} \dfrac{1}{r^2}\,dr\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121289/*