Electromagnetic Induction Notes for NEET, Class 12 NCERT

Introduction

A magnetic field that is changing with time induces an electric field that drives a current. Faraday and Henry discovered this in the 1830s, and it underlies all generators, transformers and electric motors. Expect 1 to 2 NEET questions; favourites are Faraday\'s law applications, motional EMF, Lenz\'s law direction, and energy stored in an inductor.

Magnetic flux

Flux through an area:

Φ_{B} = \int B \cdot d A .

For a uniform field through a flat area: $Φ_{B} = B A cos θ$ . Unit: weber (Wb) = T·m².

Magnetic flux through a flat area: Phi = B A cos theta. Maximum when normal is parallel to B; zero when perpendicular.

B: 0.50 T

Area A: 100 cm²

θ between normal and B: 30°

Magnetic flux Φ

4.330e-3 Wb

Φ = B \cdot A = B A cos θ

Faraday's law of induction

The induced EMF in a closed loop equals the rate of change of magnetic flux through it:

ϵ = - N \frac{d Φ _{B}}{d t} .

N is the number of turns. The negative sign captures the direction (Lenz's law).

Induced EMF in a coil of N turns when flux changes by ΔΦ over time Δt.

Turns N: 50

ΔΦ: 5.00 mWb

Δt: 100 ms

Induced EMF

2.500 V

ϵ = - N \frac{ΔΦ}{Δ t}

Lenz's law

The direction of the induced current is such that it opposes the change in flux that produced it. Equivalent to energy conservation: if the induced current aided the change, energy would be created from nothing.

A bar magnet moves near a closed coil. Lenz's law says the induced current opposes the change in flux.

Flux change: increasing (into the loop, say from top)

Induced field direction: OPPOSITE to B (so out of the top)

Coil acts as: N pole faces the magnet (to repel)

ϵ = - \frac{d Φ}{d t}

Motional EMF

A conducting rod of length L sliding with velocity v in a perpendicular magnetic field B sweeps out new area per second equal to L v. This rate of new flux is:

ϵ = B Lv .

If the rod is part of a closed circuit of resistance R, the induced current is $I = B Lv / R$ , and the rod feels an opposing magnetic force $F = B I L$ .

A conducting rod of length L slides on rails with velocity v in a perpendicular field B. EMF = B L v.

B: 0.50 T

L: 0.50 m

v: 2.00 m/s

Circuit R: 0.50 Ω

EMF

0.500 V

ϵ = B Lv

1.000 A

Drag F

0.250 N

Power P

0.500 W

Eddy currents

Bulk pieces of conductor moving in a changing flux develop swirling current patterns called eddy currents. They dissipate energy as heat. Useful applications: induction cooking, magnetic braking, metal detection. Undesirable in transformer cores, where laminations are used to break up the eddies.

Practice these on the timed test

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Self-inductance

When the current through a coil changes, the changing self-flux induces a back EMF in the coil:

ϵ_{self} = - L \frac{d I}{d t} .

L is the self-inductance, in henries (H). For a long solenoid:

L = \frac{μ _{0} N ^{2} A}{l} .

Self-inductance of a long solenoid with N turns, area A and length l. The faster the current changes, the bigger the back EMF.

Turns N: 500

Area A: 10.0 cm²

Length l: 20.0 cm

di/dt: 2 A/s

Self-inductance L

1.571 mH

L = \frac{μ _{0} N ^{2} A}{l}

Back EMF

0.003 V

∣ ϵ ∣ = L d i / d t

Mutual inductance

When current in one coil changes, it induces an EMF in a neighbouring coil:

ϵ_{2} = - M \frac{d I _{1}}{d t} .

M is the mutual inductance. Reciprocity: M_12 = M_21. Two solenoids one inside the other have $M = μ_{0} N_{1} N_{2} A / l$ . Coupling coefficient $k = M / L_{1} L_{2}$ , with k = 1 for perfect coupling.

Two coils linked by flux: changing current in one induces an EMF in the other. Mutual inductance M is the coupling constant.

N₁ (primary): 500

N₂ (secondary): 200

Common A: 10.0 cm²

Length l: 20 cm

di₁/dt: 2 A/s

Mutual inductance M

0.628 mH

M = \frac{μ _{0} N _{1} N _{2} A}{l}

Induced EMF in secondary

0.001 V

∣ ϵ_{2} ∣ = M d i_{1} / d t

Energy stored in an inductor

Building current up from zero requires work against the back EMF:

U = \frac{1}{2} L I^{2} .

Energy density in the magnetic field (in vacuum):

u = \frac{B ^{2}}{2 μ _{0}} .

An inductor stores energy in its magnetic field. Same form as the kinetic energy formula (½ m v²).

Inductance L: 50.0 mH

Current I: 2.00 A

Stored energy

100.000 mJ

U = \frac{1}{2} L I^{2}

Worked NEET problems

NEET-style problem · Faraday

Question

A coil of 100 turns has flux changing from 2 mWb to 5 mWb in 0.1 s. Find induced EMF.

Solution

∣ ϵ ∣ = N ΔΦ/Δ t = 100 \times (3 \times 1 0^{- 3}) /0.1 = 3 V .

NEET-style problem · Motional

Question

A 0.5 m rod slides at 4 m/s perpendicular to a 0.2 T field. Find EMF.

Solution

ϵ = B Lv = 0.2 \times 0.5 \times 4 = 0.4 V .

NEET-style problem · Lenz

Question

A bar magnet's N pole approaches a coil. The induced current in the coil (viewed from the magnet side) flows:

Solution

Counter-clockwise. The coil's near face becomes a N pole to repel the approaching N pole.

NEET-style problem · Self-induction

Question

An inductor of L = 50 mH has its current changing at 100 A/s. Find back EMF.

Solution

∣ ϵ ∣ = L d I / d t = 0.05 \times 100 = 5 V .

NEET-style problem · Energy

Question

L = 0.1 H, I = 5 A. Find energy stored.

Solution

U = \frac{1}{2} L I^{2} = \frac{1}{2} \times 0.1 \times 25 = 1.25 J .

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Summary cheat sheet

Flux: $Φ = B A cos θ$ .
Faraday: $ϵ = - N d Φ/ d t$ .
Lenz: induced current opposes the change in flux.
Motional EMF: $ϵ = B Lv$ .
Self: $ϵ = - L d I / d t$ , $L = μ_{0} N^{2} A / l$ (solenoid).
Mutual: $ϵ_{2} = - M d I_{1} / d t$ .
Energy: $U = \frac{1}{2} L I^{2}$ .
Energy density: $u = B^{2} / (2 μ_{0})$ .

Next: try the interactive widgets for Faraday, motional EMF and inductors, or work through the 32 NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.

Frequently asked questions

How many questions come from Electromagnetic Induction in NEET 2027?

You can expect 1 to 2 questions in NEET 2027. The chapter has high PYQ frequency. Faraday's law applications, motional EMF, Lenz's law direction, self-inductance and energy stored in an inductor are favourites.

What is Faraday's law of induction?

Whenever the magnetic flux through a closed loop changes, an EMF is induced in the loop equal to minus the rate of change of flux. epsilon equals minus d Phi over dt. For N turns, multiply by N. The induced EMF drives a current if the loop is closed.

What is Lenz's law?

The direction of the induced current is such that it OPPOSES the change in flux that produced it. This is the meaning of the negative sign in Faraday's law. Lenz's law follows from energy conservation: if the induced current aided the change, you could create energy out of nothing.

What is motional EMF?

A conducting rod of length L moving with velocity v perpendicular to a magnetic field B (with v perpendicular to L) develops EMF epsilon equals B L v across its ends. This is induced EMF without any time-varying field; the change of flux comes from the rod sweeping out new area.

What are eddy currents?

Currents induced in bulk pieces of conductor by a changing flux. They form swirling loops, hence the name. Eddy currents heat up the conductor, dissipating energy. They are useful in induction stoves and magnetic braking, and undesirable in transformer cores (laminations reduce them).

What is self-inductance?

When the current through a coil changes, the changing flux through itself induces a back EMF. epsilon equals minus L di over dt. L is the self-inductance, in henries (H). For a long solenoid, L equals mu_0 N squared A over length.

What is the energy stored in an inductor?

Building up current I from zero in an inductor requires work, which is stored in the magnetic field. U equals half L I squared. Energy density (in vacuum) is u equals B squared over (2 mu_0).