---
title: "Two long, insulated, straight wires lie in the \\(xy\\)-plane along the coordinate axes, each carrying a current \\(I\\) in the positive direction (along \\(+x\\) and \\(+y\\), respectively). Four points—\\(P_1(a,a)\\), \\(P_2(-a,a)\\), \\(P_3(-a,-a)\\), and \\(P_4(a,-a)\\)—are located in the four quadrants at equal distances \\(a\\) from both wires. At which pair of points is the net magnetic field magnitude greatest, and what is the direction of the net magnetic field at point \\(P_2\\)?"
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url: "https://nerd-notes.com/ubq/118596/"
date_modified: "2026-08-04T08:11:34+00:00"
---

# Two long, insulated, straight wires lie in the \(xy\)-plane along the coordinate axes, each carrying a current \(I\) in the positive direction (along \(+x\) and \(+y\), respectively). Four points—\(P_1(a,a)\), \(P_2(-a,a)\), \(P_3(-a,-a)\), and \(P_4(a,-a)\)—are located in the four quadrants at equal distances \(a\) from both wires. At which pair of points is the net magnetic field magnitude greatest, and what is the direction of the net magnetic field at point \(P_2\)?

Two long, insulated, straight wires lie in the \(xy\)-plane along the coordinate axes, each carrying a current \(I\) in the positive direction (along \(+x\) and \(+y\), respectively). Four points—\(P_1(a,a)\), \(P_2(-a,a)\), \(P_3(-a,-a)\), and \(P_4(a,-a)\)—are located in the four quadrants at equal distances \(a\) from both wires. At which pair of points is the net magnetic field magnitude greatest, and what is the direction of the net magnetic field at point \(P_2\)?

![A two-dimensional Cartesian coordinate plane showing two perpendicular, insulated straight wires carrying current. One wire lies along the horizontal x-axis with an arrow labeled I pointing to the right (+x direction). The second wire lies along the vertical y-axis with an arrow labeled I pointing upward (+y direction). The plane is divided into four quadrants containing four points, each labeled with a black dot: point P_1 is in Quadrant I at position (a, a); point P_2 is in Quadrant II at position (-a, a); point P_3 is in Quadrant III at position (-a, -a); and point P_4 is in Quadrant IV at position (a, -a). Dashed grid lines extend from each point to the axes, indicating equal distance a from both wires. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831093-l4QAiY.jpg)

- **A.** \(P_1\) and \(P_3\); Out of the page
- **B.** \(P_2\) and \(P_4\); Out of the page
- **C.** \(P_2\) and \(P_4\); Into the page
- **D.** \(P_1\) and \(P_3\); Into the page

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118596/*