---
title: "Hall voltage and mobility in silver"
subject: "Engineering Physics"
chapter: 8
key: "semester_1/engineering_physics:hall-numerical-silver-foil"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/hall-numerical-silver-foil
site: BCT Engineering
---

# Hall voltage and mobility in silver

Engineering Physics · Chapter 8: Electromagnetism

- Asked in: 2070 Asar, 5 marks
- Video: [Hall Voltage in a Silver  Metal # Lecture 10](https://www.youtube.com/watch?v=b4L-RADucrY) — PHYSICS GURU
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/hall-numerical-silver-foil
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-8

## Question

In a Hall experiment, a current of 25A is passed through a long foil of silver, which is 0.1 mm thick and 3 m long. Calculate the Hall voltage produced across the width by a flux of 1.4 Wb/m². If the conduction of silver is 6.8×10⁷ mho/m, estimate the mobility of the electrons in silver.

## Short answer

Using n = 5.86×10²⁸ m⁻³, Hall voltage V_H = IB/(n e t) = 3.73×10⁻⁵ V (≈ 37 μV). Electron mobility μ = σ/(n e) ≈ 7.2×10⁻³ m²V⁻¹s⁻¹.

## Answer

**Formulas:** V_H = IB/(n e t) and, for mobility, μ = σ R_H = σ/(ne).

**Assumption:** the question does not give n, so I use the standard value for silver, one free electron per atom: **n = 5.86×10²⁸ m⁻³**. The foil length (3 m) is not needed. Here t = 0.1 mm, I = 25 A, B = 1.4 T, σ = 6.8×10⁷ S/m.

#### Hall voltage
```text
n e t = 5.86×10²⁸ × 1.602×10⁻¹⁹ × 1×10⁻⁴ = 9.388×10⁵
V_H   = (25 × 1.4) / 9.388×10⁵
      = 35 / 9.388×10⁵
      = 3.73×10⁻⁵ V
```

#### Mobility
```text
R_H = 1/(ne) = 1 / (5.86×10²⁸ × 1.602×10⁻¹⁹) = 1.065×10⁻¹⁰ m³/C
μ   = σ R_H  = 6.8×10⁷ × 1.065×10⁻¹⁰
    = 7.24×10⁻³ m²/(V·s)
```

**Answer: V_H ≈ 37 μV; electron mobility ≈ 7.2×10⁻³ m²V⁻¹s⁻¹** (about 72 cm²/V·s).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The question does not give n for silver. What is assumed?
   A. n = 10²⁸ m⁻³ for every metal
   B. One free electron per atom, n = 5.86×10²⁸ m⁻³
   C. n is found from the foil length
   D. n is found from the current alone
   Answer: B. The standard value for silver is used. (Key point: Missing data)

2. V_H = IB/(net) with I = 25 A, B = 1.4 T, t = 0.1 mm gives about:
   A. 37 μV
   B. 37 mV
   C. 3.7 μV
   D. 0.37 V
   Answer: A. 35/9.388×10⁵ ≈ 3.73×10⁻⁵ V. (Key point: Hall voltage)

3. Electron mobility is found from:
   A. μ = R_H/σ
   B. μ = σ n e
   C. μ = σR_H = σ/(ne)
   D. μ = σ t B
   Answer: C. Mobility = conductivity × Hall coefficient. (Key point: Mobility)

4. Which given quantity is not needed?
   A. The thickness 0.1 mm
   B. The current 25 A
   C. The conductivity 6.8×10⁷ S/m
   D. The foil length of 3 m
   Answer: D. V_H depends on thickness, not length. (Key point: Unused data)

## Related in Engineering Physics

- [Drift velocity from Hall experiment](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Ahall-numerical-conductor-drift-velocity) — Engineering Physics, chapter 8
- [Hall voltage and mobility, copper strip](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Ahall-numerical-copper-strip-three-cm) — Engineering Physics, chapter 8, asked 2×
- [Hall voltage and mobility, wide copper strip](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Ahall-numerical-copper-strip-two-cm) — Engineering Physics, chapter 8, asked 2×
- [Hall voltage, coefficient and mobility](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Ahall-numerical-copper-strip-thin) — Engineering Physics, chapter 8
- [Hall effect, coefficient and mobility](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Ahall-effect-coefficient-mobility-conductivity) — Engineering Physics, chapter 8
- [Hall voltage and type of carriers](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Ahall-effect-voltage-carrier-type) — Engineering Physics, chapter 8, asked 2×

## Related in other subjects

- [Iron ring current for 0.82 Wb air-gap flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Airon-ring-air-gap-0-82-wb) — Electrical Machine, chapter 1, asked 2×
- [Iron ring current for 0.8 Wb air-gap flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Airon-ring-air-gap-0-8-wb) — Electrical Machine, chapter 1, asked 2×
- [Core with 4 mm air gap: inductance and flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Acircular-core-4mm-gap-inductance-flux) — Electrical Machines, chapter 1
- [Classical: inductor current and voltage at 10 ms](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aclassical-inductor-current-20v-10v-30ohm) — Electrical Circuit Theory, chapter 3