---
title: "A conducting bar of mass \\(m\\) and length \\(\\ell\\) slides down two frictionless parallel conducting rails inclined at an angle \\(\\theta\\) above the horizontal. The rails are separated by a distance \\(\\ell\\) and are connected at the top by a resistor of resistance \\(R\\), forming a closed circuit. A uniform magnetic field of magnitude \\(B\\) is directed perpendicular to the plane of the rails. If the electrical resistance of the bar and rails is negligible, which of the following expressions represents the terminal speed \\(v_{\\text{term}}\\) of the bar?"
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url: "https://nerd-notes.com/ubq/121323/"
date_modified: "2026-08-23T04:59:42+00:00"
---

# A conducting bar of mass \(m\) and length \(\ell\) slides down two frictionless parallel conducting rails inclined at an angle \(\theta\) above the horizontal. The rails are separated by a distance \(\ell\) and are connected at the top by a resistor of resistance \(R\), forming a closed circuit. A uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. If the electrical resistance of the bar and rails is negligible, which of the following expressions represents the terminal speed \(v_{\text{term}}\) of the bar?

A conducting bar of mass \(m\) and length \(\ell\) slides down two frictionless parallel conducting rails inclined at an angle \(\theta\) above the horizontal. The rails are separated by a distance \(\ell\) and are connected at the top by a resistor of resistance \(R\), forming a closed circuit. A uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. If the electrical resistance of the bar and rails is negligible, which of the following expressions represents the terminal speed \(v_{\text{term}}\) of the bar?

![A schematic diagram showing an inclined plane angled at \(\theta\) above a horizontal base line. Two parallel straight lines representing conducting rails run along the incline, separated by distance \(\ell\). A zig-zag resistor symbol labeled \(R\) connects the top ends of the two rails. A solid straight bar of mass \(m\) and length \(\ell\) lies across both rails perpendicular to them. An arrow pointing down the incline near the bar is labeled \(v\). Four evenly spaced circled dots distributed between the rails represent a uniform magnetic field \(\vec{B}\) directed perpendicularly outward from the inclined plane. An angle arc at the bottom left between the horizontal base and the incline is labeled \(\theta\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461182-Yai32D.jpg)

- **A.** \(v_{\text{term}} = \dfrac{mg R \cos\theta}{B^2 \ell^2}\)
- **B.** \(v_{\text{term}} = \dfrac{mg R}{B^2 \ell^2 \sin\theta}\)
- **C.** \(v_{\text{term}} = \dfrac{mg R \sin\theta}{B^2 \ell^2}\)
- **D.** \(v_{\text{term}} = \dfrac{mg R \tan\theta}{B^2 \ell^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121323/*