---
title: "A thin, rigid square loop of wire with side length \\(L\\) lies in the \\(xy\\)-plane and carries a steady counterclockwise current \\(I\\). Points \\(P_1\\), \\(P_2\\), and \\(P_3\\) lie along the diagonal line connecting the center of the loop to its upper-right corner, where \\(P_1\\) is at the center, \\(P_2\\) is halfway along the diagonal to the corner, and \\(P_3\\) is very close to the corner. Which of the following correctly pairs the ranking of the magnetic field magnitudes \\(B_1\\), \\(B_2\\), and \\(B_3\\) at these points with the magnitude of the magnetic field \\(B_1\\) at the center of the loop?"
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url: "https://nerd-notes.com/ubq/118626/"
date_modified: "2026-08-04T08:12:17+00:00"
---

# A thin, rigid square loop of wire with side length \(L\) lies in the \(xy\)-plane and carries a steady counterclockwise current \(I\). Points \(P_1\), \(P_2\), and \(P_3\) lie along the diagonal line connecting the center of the loop to its upper-right corner, where \(P_1\) is at the center, \(P_2\) is halfway along the diagonal to the corner, and \(P_3\) is very close to the corner. Which of the following correctly pairs the ranking of the magnetic field magnitudes \(B_1\), \(B_2\), and \(B_3\) at these points with the magnitude of the magnetic field \(B_1\) at the center of the loop?

A thin, rigid square loop of wire with side length \(L\) lies in the \(xy\)-plane and carries a steady counterclockwise current \(I\). Points \(P_1\), \(P_2\), and \(P_3\) lie along the diagonal line connecting the center of the loop to its upper-right corner, where \(P_1\) is at the center, \(P_2\) is halfway along the diagonal to the corner, and \(P_3\) is very close to the corner. Which of the following correctly pairs the ranking of the magnetic field magnitudes \(B_1\), \(B_2\), and \(B_3\) at these points with the magnitude of the magnetic field \(B_1\) at the center of the loop?

![A planar square loop of side length L centered at the origin of an xy-plane. Arrows along the four straight segments show a counterclockwise current I. A dashed diagonal line extends from the origin at (0,0) to the upper-right corner at (L/2, L/2). Point P_1 is located at the center (0,0). Point P_2 is located on the dashed diagonal halfway between the center and the upper-right corner. Point P_3 is located on the dashed diagonal near the upper-right corner. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831137-FG2gqr.jpg)

- **A.** Ranking: \(B_3 > B_2 > B_1\) ; Field at center: \(B_1 = \dfrac{2\sqrt{2}\mu_0 I}{\pi L}\)
- **B.** Ranking: \(B_1 > B_2 > B_3\) ; Field at center: \(B_1 = \dfrac{2\sqrt{2}\mu_0 I}{\pi L}\)
- **C.** Ranking: \(B_3 > B_2 > B_1\) ; Field at center: \(B_1 = \dfrac{\sqrt{2}\mu_0 I}{\pi L}\)
- **D.** Ranking: \(B_1 = B_2 = B_3\) ; Field at center: \(B_1 = \dfrac{4\mu_0 I}{\pi L}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118626/*