---
title: "A conducting bar of length \\(L\\) slides to the right with constant speed \\(v\\) along two parallel conducting rails in a region of uniform magnetic field of magnitude \\(B\\) directed perpendicular to the plane of the rails. In steady state, charges within the moving bar separate until dynamic equilibrium is reached. Which of the following correctly pairs the magnitude of the induced electromotive force \\(\\mathcal{E}\\) across the bar with the magnitude of the electric field \\(E\\) inside the bar?"
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url: "https://nerd-notes.com/ubq/118711/"
date_modified: "2026-08-04T08:13:50+00:00"
---

# A conducting bar of length \(L\) slides to the right with constant speed \(v\) along two parallel conducting rails in a region of uniform magnetic field of magnitude \(B\) directed perpendicular to the plane of the rails. In steady state, charges within the moving bar separate until dynamic equilibrium is reached. Which of the following correctly pairs the magnitude of the induced electromotive force \(\mathcal{E}\) across the bar with the magnitude of the electric field \(E\) inside the bar?

A conducting bar of length \(L\) slides to the right with constant speed \(v\) along two parallel conducting rails in a region of uniform magnetic field of magnitude \(B\) directed perpendicular to the plane of the rails. In steady state, charges within the moving bar separate until dynamic equilibrium is reached. Which of the following correctly pairs the magnitude of the induced electromotive force \(\mathcal{E}\) across the bar with the magnitude of the electric field \(E\) inside the bar?

![A top-down view showing two parallel horizontal conducting rails separated vertically by a distance L. A straight vertical conducting bar of length L bridges the rails. A horizontal arrow labeled v points to the right from the center of the bar. A uniform magnetic field perpendicular to the page is indicated by a grid of vector symbols labeled B. No other labels, lines, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831230-1TykNk.jpg)

- **A.** Induced EMF: \(\mathcal{E} = \dfrac{1}{2} BLv\) ; Electric Field: \(E = \dfrac{1}{2} vB\)
- **B.** Induced EMF: \(\mathcal{E} = BLv\) ; Electric Field: \(E = vB\)
- **C.** Induced EMF: \(\mathcal{E} = BLv\) ; Electric Field: \(E = 0\)
- **D.** Induced EMF: \(\mathcal{E} = BL^2v\) ; Electric Field: \(E = BLv\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118711/*