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title: "A Hall effect probe consists of a thin rectangular semiconductor wafer of width \\(w\\) and thickness \\(t\\). A constant current \\(I\\) is maintained through the length of the wafer, and a uniform magnetic field \\(\\vec{B}\\) is directed perpendicular to its flat face, as shown. The probe measures an unknown magnetic field by recording the induced Hall potential difference \\(V_H\\) across the width \\(w\\). Two candidate semiconductor materials are considered for the probe: Material 1 has charge carrier concentration \\(n_1\\), and Material 2 has charge carrier concentration \\(n_2\\), where \\(n_1 < n_2\\). Assuming charge carriers in both materials have charge magnitude \\(q\\), which choice correctly describes the calibration curve of Hall voltage \\(V_H\\) versus magnetic field \\(B\\), and identifies the material that provides greater measurement sensitivity \\(S = \\left|\\dfrac{d V_H}{d B}\\right|\\)?"
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url: "https://nerd-notes.com/ubq/118598/"
date_modified: "2026-08-04T08:11:38+00:00"
---

# A Hall effect probe consists of a thin rectangular semiconductor wafer of width \(w\) and thickness \(t\). A constant current \(I\) is maintained through the length of the wafer, and a uniform magnetic field \(\vec{B}\) is directed perpendicular to its flat face, as shown. The probe measures an unknown magnetic field by recording the induced Hall potential difference \(V_H\) across the width \(w\). Two candidate semiconductor materials are considered for the probe: Material 1 has charge carrier concentration \(n_1\), and Material 2 has charge carrier concentration \(n_2\), where \(n_1 < n_2\). Assuming charge carriers in both materials have charge magnitude \(q\), which choice correctly describes the calibration curve of Hall voltage \(V_H\) versus magnetic field \(B\), and identifies the material that provides greater measurement sensitivity \(S = \left|\dfrac{d V_H}{d B}\right|\)?

A Hall effect probe consists of a thin rectangular semiconductor wafer of width \(w\) and thickness \(t\). A constant current \(I\) is maintained through the length of the wafer, and a uniform magnetic field \(\vec{B}\) is directed perpendicular to its flat face, as shown. The probe measures an unknown magnetic field by recording the induced Hall potential difference \(V_H\) across the width \(w\). Two candidate semiconductor materials are considered for the probe: Material 1 has charge carrier concentration \(n_1\), and Material 2 has charge carrier concentration \(n_2\), where \(n_1 < n_2\). Assuming charge carriers in both materials have charge magnitude \(q\), which choice correctly describes the calibration curve of Hall voltage \(V_H\) versus magnetic field \(B\), and identifies the material that provides greater measurement sensitivity \(S = \left|\dfrac{d V_H}{d B}\right|\)?

![A three-dimensional rectangular semiconductor strip lying flat in the horizontal xy-plane with length along the x-axis, width w along the y-axis, and thickness t along the vertical z-axis. A red arrow labeled I points in the positive x-direction along the length of the strip. Uniform magnetic field vectors labeled \vec{B}, drawn as three parallel vertical blue arrows pointing upward in the positive z-direction, penetrate the top flat face of the strip. Two contact terminals are attached to the opposite long side faces along the y-axis, connected by dashed measurement wires to a voltmeter labeled V_H. The width w is indicated along the y-axis, thickness t along the z-axis, and length L along the x-axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831097-Lax8ek.jpg)

- **A.** Relationship: Quadratic (\(V_H \propto B^2\)) | Material with greater sensitivity: Material 2
- **B.** Relationship: Quadratic (\(V_H \propto B^2\)) | Material with greater sensitivity: Material 1
- **C.** Relationship: Linear (\(V_H \propto B\)) | Material with greater sensitivity: Material 2
- **D.** Relationship: Linear (\(V_H \propto B\)) | Material with greater sensitivity: Material 1

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118598/*