---
title: "A thin rectangular conducting strip of width \\(w\\) and thickness \\(d\\) carries a uniform current \\(I\\) in the \\(+x\\)-direction. A uniform magnetic field \\(\\vec{B} = B_0 \\hat{k}\\) is directed perpendicular to the strip in the \\(+z\\)-direction. Due to the magnetic force on the charge carriers (each having charge magnitude \\(q\\)), a steady-state Hall potential difference \\(V_H\\) is established across the width \\(w\\) of the strip. Which of the following expressions is a correct expression for the volume charge carrier density \\(n\\) of the strip?"
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url: "https://nerd-notes.com/ubq/118584/"
date_modified: "2026-08-04T08:11:28+00:00"
---

# A thin rectangular conducting strip of width \(w\) and thickness \(d\) carries a uniform current \(I\) in the \(+x\)-direction. A uniform magnetic field \(\vec{B} = B_0 \hat{k}\) is directed perpendicular to the strip in the \(+z\)-direction. Due to the magnetic force on the charge carriers (each having charge magnitude \(q\)), a steady-state Hall potential difference \(V_H\) is established across the width \(w\) of the strip. Which of the following expressions is a correct expression for the volume charge carrier density \(n\) of the strip?

A thin rectangular conducting strip of width \(w\) and thickness \(d\) carries a uniform current \(I\) in the \(+x\)-direction. A uniform magnetic field \(\vec{B} = B_0 \hat{k}\) is directed perpendicular to the strip in the \(+z\)-direction. Due to the magnetic force on the charge carriers (each having charge magnitude \(q\)), a steady-state Hall potential difference \(V_H\) is established across the width \(w\) of the strip. Which of the following expressions is a correct expression for the volume charge carrier density \(n\) of the strip?

![An isometric 3D diagram showing a thin rectangular slab of conducting material oriented parallel to the xy-plane. The slab has length along the x-axis, width w along the y-axis, and thickness d along the z-axis. An arrow labeled I points in the +x-direction along the top surface to indicate current flow. Three vertical upward arrows labeled B_0 point in the +z-direction passing through the slab. A potential difference V_H is indicated across the width w along the y-axis with dashed leads connected to opposite edges parallel to the y-axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831087-LhjJ55.jpg)

- **A.** \(n = \dfrac{I B_0}{q w V_H}\)
- **B.** \(n = \dfrac{I B_0 w}{q d^2 V_H}\)
- **C.** \(n = \dfrac{I B_0}{q d V_H}\)
- **D.** \(n = \dfrac{2 I B_0}{q d V_H}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118584/*