---
title: "A long, straight wire carries a constant electric current \\(I\\). Ampère’s law, \\(\\oint \\vec{B} \\cdot d\\vec{\\ell} = \\mu_0 I_{\\text{enc}}\\), is used to calculate the magnitude of the magnetic field at a distance \\(r\\) from the center of the wire. Which of the following correctly explains why a circular Amperian loop centered on the wire is chosen and correctly interprets the meaning of \\(I_{\\text{enc}}\\)?"
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url: "https://nerd-notes.com/ubq/118512/"
date_modified: "2026-08-04T08:11:12+00:00"
---

# A long, straight wire carries a constant electric current \(I\). Ampère’s law, \(\oint \vec{B} \cdot d\vec{\ell} = \mu_0 I_{\text{enc}}\), is used to calculate the magnitude of the magnetic field at a distance \(r\) from the center of the wire. Which of the following correctly explains why a circular Amperian loop centered on the wire is chosen and correctly interprets the meaning of \(I_{\text{enc}}\)?

A long, straight wire carries a constant electric current \(I\). Ampère's law, \(\oint \vec{B} \cdot d\vec{\ell} = \mu_0 I_{\text{enc}}\), is used to calculate the magnitude of the magnetic field at a distance \(r\) from the center of the wire. Which of the following correctly explains why a circular Amperian loop centered on the wire is chosen and correctly interprets the meaning of \(I_{\text{enc}}\)?

![A vertical thin straight wire carrying an upward current labeled I. A horizontal dashed circle of radius r is centered on the wire, representing an Amperian loop. At a point on the circle, a small tangent arrow labeled B and a small tangent arrow labeled d\ell both point in the counterclockwise direction around the circle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831072-qyf1JT.jpg)

- **A.** A circular loop is chosen because the magnetic field magnitude varies linearly around the loop, causing the integral to evaluate to zero; \(I_{\text{enc}}\) represents the total current induced along the loop.
- **B.** A circular loop is chosen because the electric field is zero everywhere along the path; \(I_{\text{enc}}\) represents the total electric charge contained within the sphere bounded by the loop.
- **C.** A circular loop is chosen because the magnitude of \(\vec{B}\) is constant along the path and \(\vec{B}\) is everywhere parallel to \(d\vec{\ell}\), allowing the integral to simplify to \(B(2\pi r)\); \(I_{\text{enc}}\) represents the net current passing through the surface bounded by the loop.
- **D.** A circular loop is chosen because the magnitude of \(\vec{B}\) is constant along the path and \(\vec{B}\) is everywhere perpendicular to \(d\vec{\ell}\); \(I_{\text{enc}}\) represents the current flowing around the perimeter of the loop.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118512/*