---
title: "A conducting bar of length \\(\\ell\\) slides to the right at a constant velocity \\(\\vec{v}\\) along horizontal, frictionless parallel conducting rails situated in a uniform magnetic field \\(\\vec{B}\\) directed into the page. The rails are connected at the left end by a resistor of resistance \\(R\\). An external force \\(\\vec{F}_{\\text{app}}\\) pulls the bar to maintain its constant velocity. Which of the following correctly identifies the direction of the magnetic force \\(\\vec{F}_B\\) exerted on the moving bar and compares the magnitude of the applied force \\(F_{\\text{app}}\\) to the magnitude of the magnetic force \\(F_B\\)?"
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url: "https://nerd-notes.com/ubq/118694/"
date_modified: "2026-08-04T08:13:47+00:00"
---

# A conducting bar of length \(\ell\) slides to the right at a constant velocity \(\vec{v}\) along horizontal, frictionless parallel conducting rails situated in a uniform magnetic field \(\vec{B}\) directed into the page. The rails are connected at the left end by a resistor of resistance \(R\). An external force \(\vec{F}_{\text{app}}\) pulls the bar to maintain its constant velocity. Which of the following correctly identifies the direction of the magnetic force \(\vec{F}_B\) exerted on the moving bar and compares the magnitude of the applied force \(F_{\text{app}}\) to the magnitude of the magnetic force \(F_B\)?

A conducting bar of length \(\ell\) slides to the right at a constant velocity \(\vec{v}\) along horizontal, frictionless parallel conducting rails situated in a uniform magnetic field \(\vec{B}\) directed into the page. The rails are connected at the left end by a resistor of resistance \(R\). An external force \(\vec{F}_{\text{app}}\) pulls the bar to maintain its constant velocity. Which of the following correctly identifies the direction of the magnetic force \(\vec{F}_B\) exerted on the moving bar and compares the magnitude of the applied force \(F_{\text{app}}\) to the magnitude of the magnetic force \(F_B\)?

![A horizontal rectangular circuit loop formed by two parallel rails extending along the x-axis and connected on the left by a vertical resistor labeled R. A straight vertical conducting bar of length \(\ell\) spans across the rails. An arrow labeled v points horizontally to the right from the bar's midpoint. An arrow labeled F_app points horizontally to the right from the bar. Evenly spaced cross symbols inside circles, labeled B, indicate a uniform magnetic field directed into the page throughout the loop interior and surroundings. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831227-cTIIVO.jpg)

- **A.** Direction of \(\vec{F}_B\): To the left | Magnitude comparison: \(F_{\text{app}} = F_B\)
- **B.** Direction of \(\vec{F}_B\): To the left | Magnitude comparison: \(F_{\text{app}} > F_B\)
- **C.** Direction of \(\vec{F}_B\): To the right | Magnitude comparison: \(F_{\text{app}} = F_B\)
- **D.** Direction of \(\vec{F}_B\): To the right | Magnitude comparison: \(F_{\text{app}} > F_B\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118694/*