---
title: "A long, straight wire carries a constant current \\(I\\) out of the page. A student considers using Ampère’s law with a square closed path of side length \\(2r\\) centered on the wire, in the plane of the page, to find the magnetic field magnitude at a distance \\(r\\) from the wire. Which of the following statements and justifications correctly evaluates the student’s proposal?"
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url: "https://nerd-notes.com/ubq/121223/"
date_modified: "2026-08-23T04:58:56+00:00"
---

# A long, straight wire carries a constant current \(I\) out of the page. A student considers using Ampère’s law with a square closed path of side length \(2r\) centered on the wire, in the plane of the page, to find the magnetic field magnitude at a distance \(r\) from the wire. Which of the following statements and justifications correctly evaluates the student’s proposal?

A long, straight wire carries a constant current \(I\) out of the page. A student considers using Ampère's law with a square closed path of side length \(2r\) centered on the wire, in the plane of the page, to find the magnetic field magnitude at a distance \(r\) from the wire. Which of the following statements and justifications correctly evaluates the student's proposal?

![A square closed path with side length labeled \(2r\) oriented symmetrically around the origin. A small circle with a solid center dot sits at the exact center of the square, labeled \(I\). A single counterclockwise arrowhead is drawn on the top horizontal segment of the square. A dashed line segment extends horizontally from the center to the right vertical edge of the square, labeled \(r\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461136-wWu524.jpg)

- **A.** Ampère's law is valid for the square path, but it cannot be directly used to algebraically solve for \(B\) because both the magnitude of \(\vec{B}\) and its angle relative to \(d\vec{\ell}\) vary along each side of the path.
- **B.** Ampère's law is not valid for the square path because Ampère's law applies strictly to closed paths that have circular symmetry around the current source.
- **C.** Ampère's law is valid for the square path and can be directly used to solve for \(B\) because the enclosed current is \(I\), allowing the line integral to simplify to \(8rB = \mu_0 I\).
- **D.** Ampère's law is valid for the square path, but it cannot be used to solve for \(B\) because the net circulation \(\oint \vec{B} \cdot d\vec{\ell}\) evaluates to zero for any non-circular closed path.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121223/*