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title: "A conducting bar of mass \\(m\\) and length \\(\\ell\\) slides on two parallel, frictionless horizontal conducting rails separated by a distance \\(\\ell\\) in a uniform vertical magnetic field of magnitude \\(B\\). The left ends of the rails are connected to an unknown resistor of resistance \\(R\\), while the electrical resistance of the bar and rails is negligible. At time \\(t = 0\\), the bar is given an initial speed \\(v_0\\) to the right and subsequently slows down due to magnetic braking. To determine the resistance \\(R\\) from a linear graph, which quantity should be plotted on the vertical axis versus time \\(t\\) on the horizontal axis, and what is the resistance \\(R\\) in terms of the magnitude of the slope \\(s\\) of the resulting best-fit line?"
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url: "https://nerd-notes.com/ubq/125061/"
date_modified: "2026-09-28T14:14:09+00:00"
---

# A conducting bar of mass \(m\) and length \(\ell\) slides on two parallel, frictionless horizontal conducting rails separated by a distance \(\ell\) in a uniform vertical magnetic field of magnitude \(B\). The left ends of the rails are connected to an unknown resistor of resistance \(R\), while the electrical resistance of the bar and rails is negligible. At time \(t = 0\), the bar is given an initial speed \(v_0\) to the right and subsequently slows down due to magnetic braking. To determine the resistance \(R\) from a linear graph, which quantity should be plotted on the vertical axis versus time \(t\) on the horizontal axis, and what is the resistance \(R\) in terms of the magnitude of the slope \(s\) of the resulting best-fit line?

A conducting bar of mass \(m\) and length \(\ell\) slides on two parallel, frictionless horizontal conducting rails separated by a distance \(\ell\) in a uniform vertical magnetic field of magnitude \(B\). The left ends of the rails are connected to an unknown resistor of resistance \(R\), while the electrical resistance of the bar and rails is negligible. At time \(t = 0\), the bar is given an initial speed \(v_0\) to the right and subsequently slows down due to magnetic braking. To determine the resistance \(R\) from a linear graph, which quantity should be plotted on the vertical axis versus time \(t\) on the horizontal axis, and what is the resistance \(R\) in terms of the magnitude of the slope \(s\) of the resulting best-fit line?

![A top-down schematic view of a rectangular conducting track on a horizontal plane. Two parallel horizontal line segments represent rails of length 4L separated by a vertical distance \ell. The left ends of the two rails are connected by a vertical line containing a resistor labeled R. A straight vertical bar of length \ell is positioned perpendicular to the rails at a distance L from the left resistor. A horizontal arrow pointing to the right originates from the center of the bar, labeled \vec{v}_0. Across the region between the rails, a regular grid of four columns and two rows of small 'x' symbols indicates a uniform magnetic field directed into the page, labeled \vec{B}. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604849-bkNiS1.jpg)

- **A.** Plot \(\dfrac{1}{v}\) on the vertical axis, and calculate \(R = \dfrac{B^2\ell^2}{2ms}\)
- **B.** Plot \(\dfrac{1}{v}\) on the vertical axis, and calculate \(R = \dfrac{B^2\ell^2}{ms}\)
- **C.** Plot \(\ln(v)\) on the vertical axis, and calculate \(R = \dfrac{B^2\ell^2}{ms}\)
- **D.** Plot \(\ln(v)\) on the vertical axis, and calculate \(R = \dfrac{2B^2\ell^2}{ms}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125061/*