---
title: "A flat, rigid rectangular conducting sheet of length \\(L\\), width \\(w\\), thickness \\(d\\), and electrical resistivity \\(\\rho\\) moves to the right with instantaneous speed \\(v\\) into a region containing a uniform magnetic field \\(B\\) directed perpendicular to its face. At an instant when a length \\(x\\) (where \\(0 < x < L\\)) of the sheet has entered the field region, the current flowing across the width \\(w\\) encounters an effective electrical resistance of \\(R = \\dfrac{\\rho w}{x d}\\). Which of the following expressions represents the magnitude of the magnetic retarding force \\(F_B\\) acting on the sheet at this instant?"
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url: "https://nerd-notes.com/ubq/118744/"
date_modified: "2026-08-04T08:14:05+00:00"
---

# A flat, rigid rectangular conducting sheet of length \(L\), width \(w\), thickness \(d\), and electrical resistivity \(\rho\) moves to the right with instantaneous speed \(v\) into a region containing a uniform magnetic field \(B\) directed perpendicular to its face. At an instant when a length \(x\) (where \(0 < x < L\)) of the sheet has entered the field region, the current flowing across the width \(w\) encounters an effective electrical resistance of \(R = \dfrac{\rho w}{x d}\). Which of the following expressions represents the magnitude of the magnetic retarding force \(F_B\) acting on the sheet at this instant?

A flat, rigid rectangular conducting sheet of length \(L\), width \(w\), thickness \(d\), and electrical resistivity \(\rho\) moves to the right with instantaneous speed \(v\) into a region containing a uniform magnetic field \(B\) directed perpendicular to its face. At an instant when a length \(x\) (where \(0 < x < L\)) of the sheet has entered the field region, the current flowing across the width \(w\) encounters an effective electrical resistance of \(R = \dfrac{\rho w}{x d}\). Which of the following expressions represents the magnitude of the magnetic retarding force \(F_B\) acting on the sheet at this instant?

![A perspective diagram showing a rectangular conducting plate moving horizontally to the right into a magnetic field region. The plate has total length L along the direction of motion, width w transverse to motion, and uniform thickness d. The right portion of the plate extends a distance x into a vertical rectangular region filled with a uniform grid of crosses labeled B, indicating a magnetic field directed perpendicular to the plate face. An arrow labeled v points to the right from the front edge of the plate. Dimension lines clearly indicate length L, width w, thickness d, and inserted distance x. No other labels, lines, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831245-N36aJH.jpg)

- **A.** \(F_B = \dfrac{B^2 w^2 v}{\rho d}\)
- **B.** \(F_B = \dfrac{B^2 w x v}{\rho d}\)
- **C.** \(F_B = \dfrac{B^2 w^2 d v}{\rho x}\)
- **D.** \(F_B = \dfrac{B^2 w x d v}{\rho}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118744/*