Electromagnetic Induction Class 12 Notes | CBSE Physics Chapter 6

Electromagnetic Induction is Chapter 6 of CBSE Class 12 Physics. This chapter explains how a changing magnetic field produces an electric current — the principle behind generators, transformers, and many modern technologies. You will learn Faraday’s laws, Lenz’s law, self and mutual inductance, and eddy currents.

This chapter carries 6–8 marks. Faraday’s laws, Lenz’s law applications, and inductance numericals are the most tested topics.

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Key Concepts

1. Magnetic Flux

Magnetic flux (Φ) through a surface is the total number of magnetic field lines passing through it.

Φ = B · A = BA cos θ

Unit: Weber (Wb) = T·m²

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2. Faraday’s Laws of Electromagnetic Induction

First Law: Whenever the magnetic flux linked with a circuit changes, an EMF is induced in the circuit.

Second Law: The magnitude of induced EMF is equal to the rate of change of magnetic flux:

ε = −dΦ/dt

For a coil of N turns: ε = −N(dΦ/dt)

The negative sign represents Lenz’s law.

Ways to Change Flux (and Induce EMF)

• Change the magnetic field strength (B)
• Change the area of the loop (A)
• Change the angle between B and the normal to the loop (θ)
• Move the conductor in the field

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3. Lenz’s Law

The direction of the induced current is such that it opposes the change in flux that produced it.

This is a consequence of the law of conservation of energy. If the induced current aided the change, it would create a perpetual motion machine — which is impossible.

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4. Motional EMF

When a conductor of length l moves with velocity v perpendicular to a magnetic field B:

ε = Blv

This is because the magnetic force on the free electrons in the conductor creates a potential difference.

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5. Self-Inductance

When current through a coil changes, the changing magnetic flux induces an EMF in the same coil that opposes the change.

ε = −L(dI/dt)

L = NΦ/I (self-inductance, unit: Henry, H)

For a solenoid: L = μ₀n²Al (n = turns per unit length, A = area, l = length)

Energy stored in an inductor: U = ½LI²

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6. Mutual Inductance

When current in one coil changes, the changing flux induces an EMF in a nearby coil.

ε₂ = −M(dI₁/dt)

M = coefficient of mutual inductance (unit: Henry)

For two coaxial solenoids: M = μ₀n₁n₂Al

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7. Eddy Currents

Eddy currents are loops of current induced in bulk conductors when exposed to changing magnetic fields.

Applications: Electromagnetic braking (trains), induction furnace, speedometers, electromagnetic damping

Disadvantage: Energy loss as heat in transformer cores. Minimised by using laminated cores.

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Important Definitions

Term	Definition
Magnetic flux	Φ = BA cos θ — total field lines through a surface (unit: Weber)
Electromagnetic induction	Production of EMF due to changing magnetic flux
Lenz’s law	Induced current opposes the change in flux that caused it
Self-inductance (L)	Property of a coil to oppose change in its own current; ε = −LdI/dt
Mutual inductance (M)	EMF induced in one coil due to changing current in another nearby coil
Eddy currents	Circulating currents induced in bulk conductors by changing magnetic fields

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Solved Examples

Example 1

A coil of 100 turns has flux changing from 0.02 Wb to 0.04 Wb in 0.1 s. Find the induced EMF.

Answer: ε = N(ΔΦ/Δt) = 100 × (0.04 − 0.02)/0.1 = 100 × 0.2 = 20 V

Example 2

A rod of length 50 cm moves at 4 m/s perpendicular to a field of 0.5 T. Find the motional EMF.

Answer: ε = Blv = 0.5 × 0.5 × 4 = 1 V

Example 3

A solenoid of self-inductance 2 H carries a current of 3 A. Find the energy stored.

Answer: U = ½LI² = ½ × 2 × 9 = 9 J

Example 4

The mutual inductance of two coils is 0.5 H. If the current in the first coil changes at 10 A/s, find the EMF in the second coil.

Answer: ε = M(dI/dt) = 0.5 × 10 = 5 V

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Important Questions for Board Exams

1-Mark

1. State Lenz’s law.
2. What is the SI unit of self-inductance?

3-Mark

1. State Faraday’s laws of electromagnetic induction. Give one application.
2. Derive the expression for motional EMF.
3. What are eddy currents? Give two applications and one disadvantage.

5-Mark

1. Derive the expression for self-inductance of a long solenoid. Also find the energy stored.
2. State and explain Faraday’s laws and Lenz’s law. Show that Lenz’s law is a consequence of conservation of energy.

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Quick Revision Points

• Φ = BA cos θ; ε = −NdΦ/dt (Faraday’s law)
• Lenz’s law: induced current opposes the cause (conservation of energy)
• Motional EMF: ε = Blv
• Self-inductance: ε = −LdI/dt; L = μ₀n²Al (solenoid); U = ½LI²
• Mutual inductance: ε₂ = −MdI₁/dt
• Eddy currents: used in braking, induction furnace; minimised by lamination

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Previous: Ch 5 — Magnetism and Matter
Next: Ch 7 — Alternating Current