---
title: "A planar square loop with sides of length \\(2a\\) carries a steady current \\(I\\). A circular loop of radius \\(a\\) in the same plane carries the same steady current \\(I\\). What is the ratio of the magnetic field magnitude at the center of the square loop to the magnetic field magnitude at the center of the circular loop, \\(\\dfrac{B_{\\text{square}}}{B_{\\text{circle}}}\\)?"
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url: "https://nerd-notes.com/ubq/121205/"
date_modified: "2026-08-23T04:58:51+00:00"
---

# A planar square loop with sides of length \(2a\) carries a steady current \(I\). A circular loop of radius \(a\) in the same plane carries the same steady current \(I\). What is the ratio of the magnetic field magnitude at the center of the square loop to the magnetic field magnitude at the center of the circular loop, \(\dfrac{B_{\text{square}}}{B_{\text{circle}}}\)?

A planar square loop with sides of length \(2a\) carries a steady current \(I\). A circular loop of radius \(a\) in the same plane carries the same steady current \(I\). What is the ratio of the magnetic field magnitude at the center of the square loop to the magnetic field magnitude at the center of the circular loop, \(\dfrac{B_{\text{square}}}{B_{\text{circle}}}\)?

![Two separate loops shown side by side in grayscale. On the left is a square loop with side length labeled \(2a\), carrying a counterclockwise current labeled \(I\) indicated by an arrow on the top edge. A dot marks the center of the square. On the right is a circular loop carrying a counterclockwise current labeled \(I\) indicated by an arrow on the top curve. A dashed radial line extends from the center dot to the circular boundary, labeled \(a\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461130-1GKx7d.jpg)

- **A.** \(\dfrac{\sqrt{2}}{\pi}\)
- **B.** \(\dfrac{2\sqrt{2}}{\pi}\)
- **C.** \(\dfrac{4}{\pi}\)
- **D.** \(\dfrac{4\sqrt{2}}{\pi}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121205/*