---
title: "Self induction and inductance of a coil"
subject: "Engineering Physics"
chapter: 8
key: "semester_1/engineering_physics:self-induction-inductance-permeability"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/self-induction-inductance-permeability
site: BCT Engineering
---

# Self induction and inductance of a coil

Engineering Physics · Chapter 8: Electromagnetism

- Asked in: 2069 Chaitra, 5 marks
- Video: [What are inductors?(self-inductance) | Electromagnetic Induction | Class 12 | Physics | Khan Academy](https://www.youtube.com/watch?v=0H3Ru8O2zG0) — Khan Academy India - English
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/self-induction-inductance-permeability
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-8

## Question

What is self induction? Define inductance of a coil. Show by calculation that the inductance of a coil depends on the permeability of the medium and the geometry of the coil.

## Short answer

Self-induction is the emf induced by a coil’s own changing current; inductance L=NΦ/I. For a long solenoid, L=μN²A/ℓ=μ₀μ_r N²A/ℓ, proving L depends on the permeability μ of the core and the coil geometry (N, A, ℓ).

## Answer

#### Self induction
When the current through a coil changes, the magnetic flux linked with the coil changes. An emf is induced in the same coil which opposes the change (Lenz's law). This is **self induction**: ε = −N dΦ/dt = −L dI/dt.

#### Inductance
The inductance of a coil is the flux linkage per unit current: **L = NΦ/I**. One henry is the inductance for which a current changing at 1 A/s induces 1 V. L is also the emf per unit rate of change of current: L = −ε/(dI/dt).

#### L depends on permeability and geometry
Take a long solenoid with N turns, length ℓ, cross-section A, filled with a core of permeability μ = μ₀μ_r.

1. Field inside (Ampere's law): B = μ N I/ℓ.
2. Flux through each turn: Φ = BA = μ N I A/ℓ.
3. Flux linkage: NΦ = μ N² A I/ℓ.
4. Inductance: L = NΦ/I

**L = μ N² A / ℓ = μ₀ μ_r N² A / ℓ**

Reading the result:
- L ∝ μ: an iron core (μ_r ~ hundreds or thousands) raises L by that factor compared with air.
- L ∝ N²/ℓ and ∝ A: it depends on the number of turns, length and area, that is, the geometry.
- I does not appear. L is fixed by the medium and the shape of the coil alone.

## Check yourself

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

1. Inductance of a coil is defined as:
   A. flux linkage per unit current, L = NΦ/I
   B. current per unit flux linkage, I/NΦ
   C. emf per unit current
   D. flux per unit area
   Answer: A. One henry gives 1 V when the current changes at 1 A/s. (Key point: Definition)

2. For a solenoid with a core of permeability μ, L is:
   A. μNA/ℓ
   B. μN²A/ℓ
   C. μN²ℓ/A
   D. N²A/(μℓ)
   Answer: B. B = μNI/ℓ, Φ = BA and L = NΦ/I. (Key point: Solenoid result)

3. Replacing an air core by iron with μ_r of hundreds changes L by:
   A. decreasing it by that factor
   B. no change
   C. increasing it by about that factor μ_r
   D. making it depend on current
   Answer: C. L ∝ μ. (Key point: Role of core)

4. Does L depend on the current I?
   A. Yes, L is proportional to I
   B. Yes, L is inversely proportional to I
   C. Only for air cores
   D. No; it depends only on geometry and the medium
   Answer: D. I cancels in L = NΦ/I. (Key point: Current dependence)

## Related in Engineering Physics

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- [Energy stored in coil, time constants](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Acoil-energy-stored-time-constants) — Engineering Physics, chapter 8

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