---
title: "A thin wire carrying a steady current \\(I\\) lies in the \\(xy\\)-plane. The wire extends along the negative \\(x\\)-axis from \\(x = -\\infty\\) to the origin \\((0,0)\\), turns \\(90^\\circ\\), and continues along the positive \\(y\\)-axis from the origin to \\(y = +\\infty\\). The unit vector \\(\\hat{k}\\) points out of the page in the \\(+z\\)-direction. What is the net magnetic field \\(\\vec{B}\\) at point \\(P\\) located at coordinates \\((d, d)\\), where \\(d > 0\\)?"
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url: "https://nerd-notes.com/ubq/121272/"
date_modified: "2026-08-23T04:59:08+00:00"
---

# A thin wire carrying a steady current \(I\) lies in the \(xy\)-plane. The wire extends along the negative \(x\)-axis from \(x = -\infty\) to the origin \((0,0)\), turns \(90^\circ\), and continues along the positive \(y\)-axis from the origin to \(y = +\infty\). The unit vector \(\hat{k}\) points out of the page in the \(+z\)-direction. What is the net magnetic field \(\vec{B}\) at point \(P\) located at coordinates \((d, d)\), where \(d > 0\)?

A thin wire carrying a steady current \(I\) lies in the \(xy\)-plane. The wire extends along the negative \(x\)-axis from \(x = -\infty\) to the origin \((0,0)\), turns \(90^\circ\), and continues along the positive \(y\)-axis from the origin to \(y = +\infty\). The unit vector \(\hat{k}\) points out of the page in the \(+z\)-direction. What is the net magnetic field \(\vec{B}\) at point \(P\) located at coordinates \((d, d)\), where \(d > 0\)?

![A Cartesian coordinate system in the xy-plane with two solid axis lines meeting at the origin \((0,0)\), labeled x on the right and y at the top. A thick solid line represents a wire running along the negative x-axis to the origin, then turning 90 degrees upward along the positive y-axis. Two open arrowheads indicate current flow: one along the negative x-axis pointing rightward labeled I, and one along the positive y-axis pointing upward labeled I. A single solid dot is located in the first quadrant at coordinates \((d, d)\), labeled P. Dashed horizontal and vertical reference lines connect point P to tick mark d on the y-axis and tick mark d on the x-axis, respectively. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461147-QIYmZG.jpg)

- **A.** \(\vec{B} = -\dfrac{\mu_0 I}{2\pi d}\,\hat{k}\)
- **B.** \(\vec{B} = +\dfrac{\sqrt{2}\mu_0 I}{4\pi d}\,\hat{k}\)
- **C.** \(\vec{B} = -\dfrac{\sqrt{2}\mu_0 I}{4\pi d}\,\hat{k}\)
- **D.** \(\vec{B} = -\dfrac{(2 + \sqrt{2})\mu_0 I}{4\pi d}\,\hat{k}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121272/*