State and explain Lenz's law.

Lenz's law states that the direction of induced current is always such that it opposes the change in magnetic flux that caused it. For example, if the flux through a coil increases (due to an approaching magnet), the induced current creates a field opposing the increase. Lenz's law is a consequence of conservation of energy.

What is self-inductance?

Self-inductance L of a coil is the property by which it opposes any change in current through itself. When current changes, the changing magnetic flux induces a back-EMF: ε = −L dI/dt. SI unit: Henry (H). Energy stored: U = ½LI².

What is the working principle of a transformer?

A transformer works on the principle of mutual induction. An alternating current in the primary coil (Np turns) creates a changing magnetic flux in the iron core, which induces an EMF in the secondary coil (Ns turns). The ratio of voltages equals the turns ratio: Vs/Vp = Ns/Np. An ideal transformer conserves power: VpIp = VsIs.

What are eddy currents? How are they minimised?

Eddy currents are circulating currents induced in bulk conductors (like iron cores) when they are subjected to changing magnetic flux. They cause energy loss as heat. They are minimised by using laminated (layered) cores — thin insulated sheets of iron — which increase resistance and reduce eddy current magnitude.

Tamil Nadu Class 12 Physics — Electromagnetic Induction Notes, Formulae & Important Questions

Exercise Solutions Available

Step-by-step answers for all textbook questions in this chapter

View Solutions →

Board Exam Weight: Electromagnetic Induction and Alternating Current carries 8–12 marks in Tamil Nadu Class 12 Physics board exams (Volume 2). NEET typically has 2–4 questions from this chapter.

1. Magnetic Flux

Magnetic flux Φ through a surface of area A when field B makes angle θ with the normal to the surface:

Φ = BA cosθ   (Weber, Wb = T·m²)

Maximum when B ⊥ surface (θ = 0°): Φ = BA
Zero when B ∥ surface (θ = 90°): Φ = 0

2. Faraday's Laws of Electromagnetic Induction

First Law

Whenever the magnetic flux through a circuit changes, an EMF is induced in the circuit.

Second Law

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

|ε| = dΦ/dt

For a coil with N turns, each experiencing the same flux change:

|ε| = N × dΦ/dt

3. Lenz's Law

The direction of the induced EMF (and induced current) is always such that it opposes the cause producing it.

Mathematically, Lenz's law gives the negative sign in Faraday's law:

ε = −N × dΦ/dt

Physical basis: Lenz's law is a direct consequence of the law of conservation of energy. If the induced current helped the change, it would create energy from nothing.

Example: A north pole approaching a coil → increasing flux → induced current creates a north pole facing the magnet (repelling it). Work must be done to push the magnet against this repulsion — this work appears as electrical energy in the circuit.

4. Self-Inductance

Self-inductance L is the constant of proportionality relating the flux linkage to current:

NΦ = LI

The induced back-EMF due to changing current:

ε = −L dI/dt

SI unit: Henry (H). 1 H = 1 V·s/A = 1 Wb/A.

Self-inductance of a solenoid:

L = μ₀N²A/l = μ₀n²Al

where n = N/l = turns per unit length, A = cross-sectional area, l = length.

Energy Stored in an Inductor

U = ½LI²

An inductor stores energy in its magnetic field (analogous to a capacitor storing energy in its electric field).

5. Mutual Inductance

When two coils are placed close to each other, changing current in coil 1 (primary) induces EMF in coil 2 (secondary):

M = N₂Φ₂₁ / I₁

Induced EMF in secondary:

ε₂ = −M dI₁/dt

SI unit: Henry (H). Mutual inductance depends on geometry (number of turns, area, separation) and medium between the coils.

6. AC Generator

Principle: Electromagnetic induction — a coil rotating in a magnetic field generates alternating EMF.

Construction: Rectangular coil (N turns, area A) rotated at angular velocity ω in a uniform field B. Slip rings and brushes collect the output.

EMF generated:

ε = NBAω sinωt = ε₀ sinωt

where ε₀ = NBAω is the peak (maximum) EMF.

The EMF varies sinusoidally — it is zero when coil is perpendicular to B and maximum when coil is parallel to B.

RMS (Root Mean Square) Values

For a sinusoidal AC:

ε_rms = ε₀ / √2 ≈ 0.707 ε₀
I_rms = I₀ / √2 ≈ 0.707 I₀

RMS values are equivalent to DC values for power calculations.

7. Transformer

Principle: Mutual induction. An AC voltage in the primary coil (Np turns) induces an AC voltage in the secondary coil (Ns turns) through a shared iron core.

Transformer Equation (Ideal)

Vs/Vp = Ns/Np

For an ideal transformer (no losses), power is conserved: VpIp = VsIs, so:

Ip/Is = Ns/Np = Vs/Vp

Step-up transformer: Ns > Np → Vs > Vp, but Is < Ip

Step-down transformer: Ns < Np → Vs < Vp, but Is > Ip

Efficiency

η = (Power output / Power input) × 100%
η = (VsIs / VpIp) × 100%

For ideal transformer: η = 100%.

Energy Losses in Real Transformers

Loss	Cause	Remedy
Copper loss (I²R)	Resistance of coil windings	Use thick copper wire
Iron/core loss (eddy currents)	Induced currents in core	Laminated core
Hysteresis loss	Repeated magnetisation/demagnetisation	Soft iron core
Flux leakage	Not all flux links both coils	Better core design

8. Worked Numericals

Numerical 1 — Induced EMF (Faraday's Law)

Problem: A coil of 100 turns and area 0.01 m² is placed in a magnetic field perpendicular to the coil. The field increases uniformly from 0 to 2 T in 0.1 s. Find the induced EMF.

Solution

Given: N = 100, A = 0.01 m², ΔB = 2 − 0 = 2 T, Δt = 0.1 s

ΔΦ = A × ΔB = 0.01 × 2 = 0.02 Wb (per turn)

ε = N × ΔΦ/Δt
ε = 100 × 0.02/0.1
ε = 100 × 0.2
ε = 20 V

The induced EMF is 20 V.

Numerical 2 — Transformer

Problem: A transformer has primary winding of 1000 turns connected to 220 V AC. The secondary has 200 turns. Find (a) secondary voltage and (b) ratio of secondary to primary current.

Solution

Given: Np = 1000, Ns = 200, Vp = 220 V

(a) Vs/Vp = Ns/Np
    Vs = Vp × Ns/Np = 220 × 200/1000 = 220 × 0.2 = 44 V

(b) Ip/Is = Ns/Np = 200/1000 = 0.2
    → Is/Ip = 5 (secondary current is 5 times primary current)

This is a step-down transformer (output voltage 44 V < input 220 V).

Numerical 3 — Self-Inductance Back EMF

Problem: A coil has self-inductance L = 2 H. The current through it changes uniformly from 0 to 4 A in 2 s. Find the induced back-EMF.

Solution

Given: L = 2 H, ΔI = 4 − 0 = 4 A, Δt = 2 s

ε = L × ΔI/Δt
ε = 2 × 4/2
ε = 2 × 2 = 4 V

The induced back-EMF is 4 V, opposing the increase in current (Lenz's law).

Numerical 4 — Energy Stored in Inductor

Problem: A coil of self-inductance 4 H carries a current of 3 A. Find the energy stored in the inductor.

Solution

Given: L = 4 H, I = 3 A

U = ½LI²
U = ½ × 4 × (3)²
U = ½ × 4 × 9
U = 18 J

The energy stored in the magnetic field of the inductor is 18 J.

9. Board Exam Model Questions

2-Mark Questions

Q1. State Lenz's law and mention its physical basis. Lenz's law: The induced current opposes the change in flux causing it (ε = −dΦ/dt). Physical basis: It is a consequence of the law of conservation of energy. If induced current aided the change, energy would be created without doing work.

Q2. Distinguish between step-up and step-down transformers.

Answer

Feature	Step-up	Step-down
Turns ratio	Ns > Np	Ns < Np
Voltage	Vs > Vp	Vs < Vp
Current	Is < Ip	Is > Ip
Use	Power transmission	Domestic supply

Q3. Define self-inductance. What is its SI unit? Self-inductance L is the property of a coil by which it opposes any change in current through it. It is defined as L = NΦ/I (flux linkage per unit current) or as L = −ε/(dI/dt) (back-EMF per unit rate of change of current). SI unit: Henry (H).

5-Mark Questions

Q4. Describe the construction and working of an AC generator. Derive the expression for the induced EMF.

Answer

An AC generator (alternator) converts mechanical energy to electrical energy.

Construction: Rectangular coil ABCD of N turns and area A, rotating in uniform field B between pole pieces of a strong magnet. The ends of the coil connect to slip rings; brushes maintain contact with the external circuit.

WorkingAs the coil rotates with angular velocity ω, the flux at time t is: Φ = NBA cosωt

By Faraday's law:

ε = −dΦ/dt = NBAω sinωt = ε₀ sinωt

where ε₀ = NBAω is the peak EMF.

The EMF is sinusoidal — zero when coil is perpendicular to field (Φ is maximum, rate of change = 0) and maximum when coil is parallel to field (Φ = 0, rate of change is maximum).

Q5. Explain the working of a transformer. Discuss the energy losses.

WorkingBased on mutual induction. AC in primary → changing flux in iron core → changing flux links secondary → EMF induced in secondary. The ratio Vs/Vp = Ns/Np holds for an ideal transformer.

Energy losses: (1) Copper loss: I²R heat in windings — reduced by using low-resistance thick conductors. (2) Eddy current loss: currents in core — reduced by laminated core. (3) Hysteresis loss: energy to reverse magnetisation — reduced by soft iron. (4) Flux leakage — reduced by better core geometry.

10. NEET Relevance

Topic	NEET Frequency
Faraday's law — induced EMF calculation	Very High
Lenz's law — direction of induced current	High
Self-inductance — back EMF, energy	High
AC generator — peak and rms EMF	Medium
Transformer — turns ratio, power	High
Eddy currents	Medium

NEET Tip: Lenz's law direction questions are common. Practice identifying: what change is happening (flux increasing or decreasing?) → what does the induced current do to oppose it? → use right-hand rule to find current direction.

11. Key Formulae Summary

Quantity	Formula
Magnetic flux	Φ = BA cosθ
Induced EMF	ε = −N dΦ/dt
Self-inductance	ε = −L dI/dt
Solenoid inductance	L = μ₀N²A/l
Energy in inductor	U = ½LI²
AC generator EMF	ε = ε₀ sinωt, ε₀ = NBAω
RMS values	V_rms = V₀/√2
Transformer voltage ratio	Vs/Vp = Ns/Np
Transformer current ratio	Is/Ip = Np/Ns

Constants: μ₀ = 4π×10⁻⁷ T·m/A

Frequently Asked Questions

First Law: Whenever the magnetic flux through a circuit changes, an EMF is induced in the circuit. Second Law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux: |ε| = dΦ/dt. For N turns: |ε| = N × dΦ/dt.