---
title: "An experiment is conducted to determine the uniform current density \\(J_0\\) inside a long, solid cylindrical conducting wire of radius \\(R\\). Miniature sensors measure the magnitude of the magnetic field \\(B\\) at various radial distances \\(r\\) from the central axis inside the wire (\\(r < R\\)). To produce a linear graph that can be used to determine \\(J_0\\), which quantities should be plotted on the vertical and horizontal axes, and what is the slope \\(m\\) of the resulting best-fit line?"
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url: "https://nerd-notes.com/ubq/124784/"
date_modified: "2026-09-28T14:11:15+00:00"
---

# An experiment is conducted to determine the uniform current density \(J_0\) inside a long, solid cylindrical conducting wire of radius \(R\). Miniature sensors measure the magnitude of the magnetic field \(B\) at various radial distances \(r\) from the central axis inside the wire (\(r < R\)). To produce a linear graph that can be used to determine \(J_0\), which quantities should be plotted on the vertical and horizontal axes, and what is the slope \(m\) of the resulting best-fit line?

An experiment is conducted to determine the uniform current density \(J_0\) inside a long, solid cylindrical conducting wire of radius \(R\). Miniature sensors measure the magnitude of the magnetic field \(B\) at various radial distances \(r\) from the central axis inside the wire (\(r < R\)). To produce a linear graph that can be used to determine \(J_0\), which quantities should be plotted on the vertical and horizontal axes, and what is the slope \(m\) of the resulting best-fit line?

![A circular cross section of a long wire centered at the origin, with outer solid boundary of radius \(R\). A solid dot marks the central axis at the center. Shading across the interior of the circle represents a uniform current density \(J_0\) directed perpendicularly out of the page. A concentric dashed circle of radius \(r\) lies entirely inside the outer boundary, where \(r < R\). A straight solid arrow extends horizontally from the center to the right edge of the dashed circle, labeled \(r\) above the arrow. A second straight solid arrow extends from the center toward the upper-right at 45 degrees to the outer solid circle, labeled \(R\) along the arrow. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604674-zv7pIP.jpg)

- **A.** Vertical axis: \(B\); Horizontal axis: \(r^2\); Slope: \(m = \dfrac{\mu_0 J_0}{2}\)
- **B.** Vertical axis: \(B\); Horizontal axis: \(r^2\); Slope: \(m = \mu_0 J_0\)
- **C.** Vertical axis: \(B\); Horizontal axis: \(r\); Slope: \(m = \dfrac{\mu_0 J_0}{2}\)
- **D.** Vertical axis: \(B\); Horizontal axis: \(r\); Slope: \(m = \mu_0 J_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124784/*