---
title: "Length of wire forming solenoid"
subject: "Engineering Physics"
chapter: 8
key: "semester_1/engineering_physics:solenoid-wire-length-numerical"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/solenoid-wire-length-numerical
site: BCT Engineering
---

# Length of wire forming solenoid

Engineering Physics · Chapter 8: Electromagnetism

- Asked in: 2070 Asar, 5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/solenoid-wire-length-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-8

## Question

A solenoid 2.6 m long and 1.3 cm in diameter carries a current of 9A. The magnetic field inside the solenoid is 20mT. Find the length of the wire forming the solenoid.

## Short answer

Turn density n = B/(μ₀I) = 1768 m⁻¹, total turns N = nℓ ≈ 4600. Wire length = N π d ≈ 188 m.

## Answer

Inside a long solenoid, B = μ₀nI, where n = N/ℓ is the number of turns per metre. Each turn is a circle of circumference πd.

**Given:** ℓ = 2.6 m, d = 1.3 cm = 0.013 m, I = 9 A, B = 20 mT = 0.020 T.

```text
n = B/(μ₀ I) = 0.020 / (4π×10⁻⁷ × 9)
  = 0.020 / 1.131×10⁻⁵
  = 1768 turns/m

N = n ℓ = 1768 × 2.6 = 4598 turns

Length of wire = N × π d = 4598 × π × 0.013
               = 4598 × 0.04084
               = 187.8 m
```

**Answer: length of wire ≈ 188 m** (about 4600 turns).

## Check yourself

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

1. Inside a long solenoid the field is:
   A. B = μ₀ N I with N total turns only
   B. B = μ₀nI, with n turns per metre
   C. B = μ₀ I / n
   D. B = nI/μ₀
   Answer: B. Ampere's law gives B = μ₀ n I. (Key point: Field inside solenoid)

2. Solving for n with B = 0.020 T, I = 9 A gives:
   A. n = B/(μ₀I) ≈ 1768 turns/m
   B. n = μ₀I/B ≈ 5.7×10⁻⁴ turns/m
   C. n = B I/μ₀ ≈ 1.4×10⁵ turns/m
   D. n = B/I ≈ 0.0022 turns/m
   Answer: A. n = 0.020/(4π×10⁻⁷ × 9). (Key point: Turns per metre)

3. How much wire does each turn use?
   A. The length ℓ of the solenoid
   B. The diameter d
   C. The area πd²/4
   D. The circumference πd of the solenoid
   Answer: D. Each turn is a circle of the solenoid's diameter. (Key point: Wire per turn)

4. The total wire length is:
   A. N × ℓ ≈ 12 000 m
   B. n × πd ≈ 72 m
   C. N × πd ≈ 4598 × 0.04084 ≈ 188 m
   D. N × d ≈ 60 m
   Answer: C. N = nℓ = 1768 × 2.6 ≈ 4598 turns, each of length πd. (Key point: Total length)

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