---
title: "A thin wire carrying a steady current \\(I\\) lies entirely in the \\(xy\\)-plane. The wire consists of three connected sections: a semi-infinite straight wire along the line \\(y = R\\) carrying current in the \\(+x\\)-direction from \\(x = -\\infty\\) to \\(x = 0\\), a semicircular arc of radius \\(R\\) centered at the origin that carries current clockwise from \\((0, R)\\) to \\((0, -R)\\), and a semi-infinite straight wire along the line \\(y = -R\\) carrying current in the \\(-x\\)-direction from \\(x = 0\\) to \\(x = -\\infty\\).  What is the magnitude of the net magnetic field at the origin in terms of \\(I\\), \\(R\\), and fundamental constants?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/121239/"
date_modified: "2026-08-23T04:58:59+00:00"
---

# A thin wire carrying a steady current \(I\) lies entirely in the \(xy\)-plane. The wire consists of three connected sections: a semi-infinite straight wire along the line \(y = R\) carrying current in the \(+x\)-direction from \(x = -\infty\) to \(x = 0\), a semicircular arc of radius \(R\) centered at the origin that carries current clockwise from \((0, R)\) to \((0, -R)\), and a semi-infinite straight wire along the line \(y = -R\) carrying current in the \(-x\)-direction from \(x = 0\) to \(x = -\infty\).

What is the magnitude of the net magnetic field at the origin in terms of \(I\), \(R\), and fundamental constants?

A thin wire carrying a steady current \(I\) lies entirely in the \(xy\)-plane. The wire consists of three connected sections: a semi-infinite straight wire along the line \(y = R\) carrying current in the \(+x\)-direction from \(x = -\infty\) to \(x = 0\), a semicircular arc of radius \(R\) centered at the origin that carries current clockwise from \((0, R)\) to \((0, -R)\), and a semi-infinite straight wire along the line \(y = -R\) carrying current in the \(-x\)-direction from \(x = 0\) to \(x = -\infty\).

What is the magnitude of the net magnetic field at the origin in terms of \(I\), \(R\), and fundamental constants?

![A schematic in the xy-plane showing coordinate axes x and y crossing at an origin labeled with an open dot. A wire carrying current I consists of three continuous segments: a horizontal top straight segment along y = R extending from the far left to (0, R) with an arrow pointing right labeled I; a semicircular arc of radius R in the right half-plane connecting (0, R) smoothly through (R, 0) to (0, -R) with a clockwise arrow labeled I; and a horizontal bottom straight segment along y = -R extending from (0, -R) to the far left with an arrow pointing left labeled I. A dashed radial line extends from the origin to (R, 0) labeled R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461138-Z1qB60.jpg)

- **A.** \(\dfrac{\mu_0 I}{4\pi R}(\pi - 2)\)
- **B.** \(\dfrac{\mu_0 I}{4\pi R}\,\pi\)
- **C.** \(\dfrac{\mu_0 I}{4\pi R}(\pi + 2)\)
- **D.** \(\dfrac{\mu_0 I}{4\pi R}(\pi + 4)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121239/*