---
title: "Four long, straight, parallel wires are perpendicular to the xy-plane and pass through the vertices of a square of side length 2d centered at the origin: (d, d), (-d, d), (-d, -d), and (d, -d). Each wire carries an identical steady current I directed out of the page in the +z-direction. Four observation points in the xy-plane are defined as P_1 at (0, 0), P_2 at (d, 0), P_3 at (0, d), and P_4 at (2d, 0). Which of the following correctly ranks the magnitudes of the net magnetic fields B_{P_1}, B_{P_2}, B_{P_3}, and B_{P_4} at these points?"
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url: "https://nerd-notes.com/ubq/124893/"
date_modified: "2026-09-28T14:11:50+00:00"
---

# Four long, straight, parallel wires are perpendicular to the xy-plane and pass through the vertices of a square of side length 2d centered at the origin: (d, d), (-d, d), (-d, -d), and (d, -d). Each wire carries an identical steady current I directed out of the page in the +z-direction. Four observation points in the xy-plane are defined as P_1 at (0, 0), P_2 at (d, 0), P_3 at (0, d), and P_4 at (2d, 0). Which of the following correctly ranks the magnitudes of the net magnetic fields B_{P_1}, B_{P_2}, B_{P_3}, and B_{P_4} at these points?

Four long, straight, parallel wires are perpendicular to the xy-plane and pass through the vertices of a square of side length 2d centered at the origin: (d, d), (-d, d), (-d, -d), and (d, -d). Each wire carries an identical steady current I directed out of the page in the +z-direction. Four observation points in the xy-plane are defined as P_1 at (0, 0), P_2 at (d, 0), P_3 at (0, d), and P_4 at (2d, 0). Which of the following correctly ranks the magnitudes of the net magnetic fields B_{P_1}, B_{P_2}, B_{P_3}, and B_{P_4} at these points?

![A Cartesian coordinate plane with horizontal x-axis and vertical y-axis intersecting at origin (0,0). Four circles with centered black dots represent identical wires carrying current out of the page, located symmetrically at (d, d), (-d, d), (-d, -d), and (d, -d). Dashed lines connect the four wire positions to outline a square centered at the origin. Four observation points are marked with solid black dots: point P_1 at (0, 0), point P_2 on the positive x-axis at (d, 0), point P_3 on the positive y-axis at (0, d), and point P_4 on the positive x-axis at (2d, 0). Tick marks on the x-axis are labeled d and 2d, and a tick mark on the y-axis is labeled d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604710-adUonj.jpg)

- **A.** \(B_{P_2} = B_{P_3} > B_{P_4} > B_{P_1}\)
- **B.** \(B_{P_1} > B_{P_2} = B_{P_3} > B_{P_4}\)
- **C.** \(B_{P_4} > B_{P_2} = B_{P_3} > B_{P_1}\)
- **D.** \(B_{P_4} > B_{P_2} = B_{P_3} = B_{P_1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124893/*