---
title: "A long, straight cylindrical wire of radius \\(R\\) carries a steady total current \\(I\\) distributed uniformly across its circular cross section. The permeability of free space is \\(\\mu_0\\). Which of the following expressions represents the total magnetic energy stored per unit length inside the volume of the wire?"
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/118758/"
date_modified: "2026-08-04T08:14:12+00:00"
---

# A long, straight cylindrical wire of radius \(R\) carries a steady total current \(I\) distributed uniformly across its circular cross section. The permeability of free space is \(\mu_0\). Which of the following expressions represents the total magnetic energy stored per unit length inside the volume of the wire?

A long, straight cylindrical wire of radius \(R\) carries a steady total current \(I\) distributed uniformly across its circular cross section. The permeability of free space is \(\mu_0\). Which of the following expressions represents the total magnetic energy stored per unit length inside the volume of the wire?

![A cross-sectional diagram showing a circular wire cross section of radius R centered at the origin. A shaded gray circle represents the full wire cross section with radius R labeled by a straight dimension line from the center to the outer perimeter, ending with an arrow and label R. Inside the wire, a dashed concentric circle of radius r is drawn, with a thin shaded circular ring of radial thickness dr around it. A radius arrow extends from the center to the dashed circle labeled r. A small circle with a dot at the center is placed near the top labeled I, indicating current directed out of the page. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-wire-cross-section-1785831251-A328bI.jpg)

- **A.** \(\dfrac{\mu_0 I^2}{4\pi}\)
- **B.** \(\dfrac{\mu_0 I^2}{8\pi}\)
- **C.** \(\dfrac{\mu_0 I^2}{12\pi}\)
- **D.** \(\dfrac{\mu_0 I^2}{16\pi}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118758/*