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title: "A conducting bar of length \\(\\ell = 0.50 \\text{ m}\\) slides with negligible friction along two parallel, horizontal conducting rails connected by a resistor of resistance \\(R = 5.0 \\text{ }\\Omega\\). A uniform magnetic field of magnitude \\(B\\) is directed perpendicular to the plane of the rails. The resulting linear graph of the net magnetic retarding force \\(F\\) versus sliding speed \\(v\\) passes through the origin and the point \\((5.0 \\text{ m/s}, 4.0 \\text{ N})\\), as shown. Based on the graph, what is the magnitude of the magnetic field \\(B\\)?"
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url: "https://nerd-notes.com/ubq/125042/"
date_modified: "2026-09-28T14:13:35+00:00"
---

# A conducting bar of length \(\ell = 0.50 \text{ m}\) slides with negligible friction along two parallel, horizontal conducting rails connected by a resistor of resistance \(R = 5.0 \text{ }\Omega\). A uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. The resulting linear graph of the net magnetic retarding force \(F\) versus sliding speed \(v\) passes through the origin and the point \((5.0 \text{ m/s}, 4.0 \text{ N})\), as shown. Based on the graph, what is the magnitude of the magnetic field \(B\)?

A conducting bar of length \(\ell = 0.50 \text{ m}\) slides with negligible friction along two parallel, horizontal conducting rails connected by a resistor of resistance \(R = 5.0 \text{ }\Omega\). A uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. The resulting linear graph of the net magnetic retarding force \(F\) versus sliding speed \(v\) passes through the origin and the point \((5.0 \text{ m/s}, 4.0 \text{ N})\), as shown. Based on the graph, what is the magnitude of the magnetic field \(B\)?

![A 2D Cartesian graph showing retarding force versus speed. The horizontal axis is labeled \(v\text{ (m/s)}\) and has evenly spaced tick marks at 0, 2.5, 5.0, 7.5, and 10.0. The vertical axis is labeled \(F\text{ (N)}\) and has evenly spaced tick marks at 0, 2.0, 4.0, 6.0, and 8.0. Light gray dashed gridlines extend across the plot area from each tick mark. A single solid black line begins at the origin \((0, 0)\) and extends linearly upward and to the right with a constant positive slope, passing precisely through grid intersections at \((2.5, 2.0)\), \((5.0, 4.0)\), \((7.5, 6.0)\), and ending at \((10.0, 8.0)\). Small filled circular markers highlight the plotted data points at each of these four coordinates and at the origin. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604814-ORJMec.jpg)

- **A.** \(4.0 \text{ T}\)
- **B.** \(5.0 \text{ T}\)
- **C.** \(8.0 \text{ T}\)
- **D.** \(16 \text{ T}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125042/*