---
title: "Two parallel, horizontal conducting rails with negligible resistance are separated by a distance \\(L\\) in a uniform magnetic field \\(\\vec{B}\\) directed into the page. Two identical conducting rods are placed perpendicular to and across the rails, forming a single closed rectangular loop. In Case 1, the two rods move toward each other, each at a constant speed \\(v\\) relative to the rails. In Case 2, both rods move to the right at the same constant speed \\(v\\) relative to the rails. Which of the following correctly gives the magnitude of the net induced electromotive force (emf) around the loop for Case 1 and Case 2?"
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url: "https://nerd-notes.com/ubq/123428/"
date_modified: "2026-09-28T11:58:33+00:00"
---

# Two parallel, horizontal conducting rails with negligible resistance are separated by a distance \(L\) in a uniform magnetic field \(\vec{B}\) directed into the page. Two identical conducting rods are placed perpendicular to and across the rails, forming a single closed rectangular loop. In Case 1, the two rods move toward each other, each at a constant speed \(v\) relative to the rails. In Case 2, both rods move to the right at the same constant speed \(v\) relative to the rails. Which of the following correctly gives the magnitude of the net induced electromotive force (emf) around the loop for Case 1 and Case 2?

Two parallel, horizontal conducting rails with negligible resistance are separated by a distance \(L\) in a uniform magnetic field \(\vec{B}\) directed into the page. Two identical conducting rods are placed perpendicular to and across the rails, forming a single closed rectangular loop. In Case 1, the two rods move toward each other, each at a constant speed \(v\) relative to the rails. In Case 2, both rods move to the right at the same constant speed \(v\) relative to the rails. Which of the following correctly gives the magnitude of the net induced electromotive force (emf) around the loop for Case 1 and Case 2?

![A top-down schematic view of two horizontal, parallel straight line segments representing rails separated vertically by a distance labeled \(L\). Two vertical thick line segments representing conducting rods span across the two rails, forming a closed rectangular region between them. The left rod is labeled 'Rod 1' and the right rod is labeled 'Rod 2'. An array of small cross symbols arranged in three rows of four spans the region, with the symbol \(\vec{B}\) positioned at the upper right. A dimension line with a double-ended vertical arrow indicates the rail separation \(L\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596713-dNNDBr.jpg)

- **A.** Case 1: \(2BLv\) ; Case 2: \(0\)
- **B.** Case 1: \(BLv\) ; Case 2: \(0\)
- **C.** Case 1: \(2BLv\) ; Case 2: \(2BLv\)
- **D.** Case 1: \(0\) ; Case 2: \(2BLv\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123428/*