---
title: "Three long, straight, parallel wires are perpendicular to the \\(xy\\)-plane and pass through the vertices of an equilateral triangle centered at the origin \\(P(0,0)\\). Wire 1 is located at \\((0, d)\\) and carries a current \\(I\\) out of the page, while Wires 2 and 3 are located at \\(\\left(-d\\dfrac{\\sqrt{3}}{2}, -\\dfrac{d}{2}\\right)\\) and \\(\\left(d\\dfrac{\\sqrt{3}}{2}, -\\dfrac{d}{2}\\right)\\), respectively, and each carry a current \\(I\\) into the page. Each wire individually produces a magnetic field of magnitude \\(B_0\\) at point \\(P\\). What are the magnitude and direction of the net magnetic field \\(\\vec{B}_{\\text{net}}\\) at point \\(P\\)?"
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url: "https://nerd-notes.com/ubq/124834/"
date_modified: "2026-09-28T14:11:37+00:00"
---

# Three long, straight, parallel wires are perpendicular to the \(xy\)-plane and pass through the vertices of an equilateral triangle centered at the origin \(P(0,0)\). Wire 1 is located at \((0, d)\) and carries a current \(I\) out of the page, while Wires 2 and 3 are located at \(\left(-d\dfrac{\sqrt{3}}{2}, -\dfrac{d}{2}\right)\) and \(\left(d\dfrac{\sqrt{3}}{2}, -\dfrac{d}{2}\right)\), respectively, and each carry a current \(I\) into the page. Each wire individually produces a magnetic field of magnitude \(B_0\) at point \(P\). What are the magnitude and direction of the net magnetic field \(\vec{B}_{\text{net}}\) at point \(P\)?

Three long, straight, parallel wires are perpendicular to the \(xy\)-plane and pass through the vertices of an equilateral triangle centered at the origin \(P(0,0)\). Wire 1 is located at \((0, d)\) and carries a current \(I\) out of the page, while Wires 2 and 3 are located at \(\left(-d\dfrac{\sqrt{3}}{2}, -\dfrac{d}{2}\right)\) and \(\left(d\dfrac{\sqrt{3}}{2}, -\dfrac{d}{2}\right)\), respectively, and each carry a current \(I\) into the page. Each wire individually produces a magnetic field of magnitude \(B_0\) at point \(P\). What are the magnitude and direction of the net magnetic field \(\vec{B}_{\text{net}}\) at point \(P\)?

![A Cartesian coordinate plane with horizontal x-axis and vertical y-axis intersecting at the origin, labeled P. Three circles of equal diameter represent the cross-sections of three parallel wires located at the vertices of an upright equilateral triangle centered at P. Wire 1 sits on the positive y-axis at (0, d) and contains a central solid black dot, indicating current directed out of the page. Wire 2 sits in the third quadrant at (-d*sqrt(3)/2, -d/2) and contains a central black cross, indicating current directed into the page. Wire 3 sits in the fourth quadrant at (d*sqrt(3)/2, -d/2) and contains a central black cross, indicating current directed into the page. Light dashed line segments connect the three wire centers to form the equilateral triangle. Thin dashed lines connect each wire center to the origin P, each labeled d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604697-tfJLq6.jpg)

- **A.** Magnitude \(2B_0\), directed along the positive \(x\)-axis
- **B.** Magnitude \(2B_0\), directed along the negative \(y\)-axis
- **C.** Magnitude \(B_0\), directed along the positive \(x\)-axis
- **D.** Magnitude zero

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124834/*