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title: "In an experiment to determine the vacuum permeability \\(\\mu_0\\), students measure the attractive magnetic force per unit length \\(F/\\ell\\) between two long, straight parallel wires carrying identical steady currents \\(I\\). The measurement is repeated for several different separation distances \\(d\\). To determine an experimental value for \\(\\mu_0\\) from a linear graph, which quantities should be plotted on the vertical and horizontal axes, and how is \\(\\mu_0\\) related to the slope \\(m\\) of the resulting best-fit line?"
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url: "https://nerd-notes.com/ubq/124799/"
date_modified: "2026-09-28T14:11:21+00:00"
---

# In an experiment to determine the vacuum permeability \(\mu_0\), students measure the attractive magnetic force per unit length \(F/\ell\) between two long, straight parallel wires carrying identical steady currents \(I\). The measurement is repeated for several different separation distances \(d\). To determine an experimental value for \(\mu_0\) from a linear graph, which quantities should be plotted on the vertical and horizontal axes, and how is \(\mu_0\) related to the slope \(m\) of the resulting best-fit line?

In an experiment to determine the vacuum permeability \(\mu_0\), students measure the attractive magnetic force per unit length \(F/\ell\) between two long, straight parallel wires carrying identical steady currents \(I\). The measurement is repeated for several different separation distances \(d\). To determine an experimental value for \(\mu_0\) from a linear graph, which quantities should be plotted on the vertical and horizontal axes, and how is \(\mu_0\) related to the slope \(m\) of the resulting best-fit line?

![Two vertical solid line segments of equal length run parallel to each other, spaced apart horizontally. On the left vertical line, an upward-pointing arrow along the line is labeled I. On the right vertical line, an identical upward-pointing arrow along the line is also labeled I. A horizontal dashed double-headed arrow spans between the two vertical lines at their midpoints and is labeled d. At the midpoint of the left line, a horizontal solid arrow points directly toward the right line and is labeled F. At the midpoint of the right line, an equal-length horizontal solid arrow points directly toward the left line and is also labeled F. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604681-CoUV9g.jpg)

- **A.** Vertical axis: \(F/\ell\); Horizontal axis: \(1/d^2\); \(\mu_0 = \dfrac{m}{2\pi I^2}\)
- **B.** Vertical axis: \(F/\ell\); Horizontal axis: \(1/d\); \(\mu_0 = \dfrac{2\pi m}{I^2}\)
- **C.** Vertical axis: \(F/\ell\); Horizontal axis: \(1/d\); \(\mu_0 = \dfrac{m}{2\pi I^2}\)
- **D.** Vertical axis: \(F/\ell\); Horizontal axis: \(1/d^2\); \(\mu_0 = \dfrac{2\pi m}{I^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124799/*