---
title: "A conducting rod of negligible resistance moves at a constant speed \\(v\\) to the right along two frictionless, parallel conducting rails separated by a distance \\(L\\). The rails have negligible resistance and are connected on the left by a resistor of resistance \\(R\\), forming a closed rectangular circuit in a uniform magnetic field of magnitude \\(B\\) directed perpendicularly into the page. In a second experiment with the same magnetic field and resistor, the rail separation is increased to \\(2L\\) and the rod is moved at a constant speed of \\(\\dfrac{v}{4}\\). What is the ratio of the induced electric current in the second experiment to the induced electric current in the first experiment, \\(\\dfrac{I_2}{I_1}\\)?"
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url: "https://nerd-notes.com/ubq/123259/"
date_modified: "2026-09-28T11:58:02+00:00"
---

# A conducting rod of negligible resistance moves at a constant speed \(v\) to the right along two frictionless, parallel conducting rails separated by a distance \(L\). The rails have negligible resistance and are connected on the left by a resistor of resistance \(R\), forming a closed rectangular circuit in a uniform magnetic field of magnitude \(B\) directed perpendicularly into the page. In a second experiment with the same magnetic field and resistor, the rail separation is increased to \(2L\) and the rod is moved at a constant speed of \(\dfrac{v}{4}\). What is the ratio of the induced electric current in the second experiment to the induced electric current in the first experiment, \(\dfrac{I_2}{I_1}\)?

A conducting rod of negligible resistance moves at a constant speed \(v\) to the right along two frictionless, parallel conducting rails separated by a distance \(L\). The rails have negligible resistance and are connected on the left by a resistor of resistance \(R\), forming a closed rectangular circuit in a uniform magnetic field of magnitude \(B\) directed perpendicularly into the page. In a second experiment with the same magnetic field and resistor, the rail separation is increased to \(2L\) and the rod is moved at a constant speed of \(\dfrac{v}{4}\). What is the ratio of the induced electric current in the second experiment to the induced electric current in the first experiment, \(\dfrac{I_2}{I_1}\)?

![A schematic showing a horizontal rectangular circuit viewed from directly above. Two parallel horizontal line segments represent rails separated by a vertical distance labeled \(L\). A vertical zigzag symbol on the left connects the left ends of the two rails and is labeled \(R\). A vertical solid line segment representing a rod spans between the two rails. A horizontal arrow pointing to the right originates from the center of the rod and is labeled \(v\). Inside and around the rectangular loop, an array of exactly twelve evenly spaced cross symbols (x) arranged in three rows of four indicates a perpendicular magnetic field, labeled \(B\). A dashed vertical line with tick marks indicates the vertical separation \(L\) between the rails. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596682-KjSf3L.jpg)

- **A.** \(\dfrac{1}{2}\)
- **B.** \(1\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123259/*