CBSE Class 12 Physics Revision Notes Chapter 6: Electromagnetic Induction

Electromagnetic induction is the production of an emf when the magnetic flux linked with a conductor changes. The chapter connects changing magnetic fields with induced current, inductance, stored magnetic energy and electricity generation.

Electromagnetic Induction explains how a changing magnetic field can produce an electromotive force in a conductor. The induced emf may result from relative motion, changing current, changing magnetic-field strength, rotation or a change in loop area.

Use these CBSE Class 12 Physics Revision Notes Chapter 6 for the 2026–27 session. Begin with magnetic flux and Faraday’s experiments. Then revise Lenz’s law, motional emf, inductance, magnetic energy and the AC generator.

Key Takeaways

• Magnetic flux: ΦB = BA cos θ measures the magnetic field passing through a surface.
• Faraday’s law: ε = −N(dΦB/dt) gives the induced emf in an N-turn coil.
• Motional emf: ε = Blv for a rod moving perpendicular to a uniform magnetic field.
• Inductor energy: U = ½LI² is stored in the magnetic field of an inductor.

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Faraday and Henry Experiments in Class 12 Physics Chapter 6 Notes

The Faraday and Henry experiments established that an electric current can be induced when the magnetic flux linked with a conductor changes.

Magnet Moving Towards or Away from a Coil

Consider a coil connected to a galvanometer.

When the north pole of a magnet moves towards the coil:

• The galvanometer shows a deflection.
• Current is induced in the coil.
• The deflection lasts only while the magnet moves.

When the magnet is held stationary:

• The galvanometer shows no deflection.
• No current is induced.

When the magnet is pulled away:

• The galvanometer deflects in the opposite direction.
• The direction of induced current reverses.

A faster motion produces a larger galvanometer deflection. This indicates a larger induced emf.

Coil Moving Relative to a Magnet

The same effect occurs when:

• The magnet remains fixed.
• The coil moves towards or away from it.

Therefore, relative motion between the magnet and coil changes the flux and produces an induced current.

Current-Carrying Coil Moving Near Another Coil

Replace the magnet with a second coil connected to a battery.

When the current-carrying coil moves towards the test coil:

• Magnetic flux through the test coil changes.
• An induced current flows.

When it moves away:

• The flux changes in the opposite manner.
• The direction of induced current reverses.

Two Stationary Coils

Relative motion is not always necessary.

Consider two stationary coils:

• One coil is connected to a battery and key.
• The other coil is connected to a galvanometer.

When the key is pressed:

• Current in the first coil rises.
• Its magnetic field changes.
• A momentary current is induced in the second coil.

When the key remains pressed:

• Current becomes steady.
• Magnetic flux becomes constant.
• The induced current becomes zero.

When the key is released:

• Current and magnetic field decrease.
• A momentary current is induced in the opposite direction.

This shows that changing current in one coil can induce emf in another coil.

Main Conclusion of the Experiments

An emf is induced whenever the magnetic flux linked with a circuit changes.

The flux may change because of:

• Relative motion between a magnet and coil
• Relative motion between two coils
• Change in current in a nearby coil
• Change in magnetic-field strength
• Change in loop area
• Change in loop orientation

Magnetic Flux in Electromagnetic Induction Class 12 Notes

Magnetic flux measures the magnetic field passing through a surface.

Magnetic Flux Through a Plane Surface

For a plane surface of area A placed in a uniform magnetic field B:

ΦB = B·A

Therefore:

ΦB = BA cos θ

Here:

• B is the magnetic-field magnitude.
• A is the surface area.
• θ is the angle between B and the area vector A.

Magnetic flux is a scalar quantity.

Area Vector

The area vector is perpendicular to the surface.

Its magnitude equals the area of the surface.

The angle in the magnetic-flux formula is measured between:

• Magnetic field B
• Area vector A

It is not measured between B and the plane of the surface.

Important Flux Cases

The flux is maximum when the plane of the loop is perpendicular to the magnetic field.

The flux is zero when the plane of the loop is parallel to the field.

Magnetic Flux Through a Non-Uniform Field

For a surface divided into small area elements:

ΦB = ΣBi·dAi

For a continuous surface:

ΦB = ∫B·dA

The SI unit of magnetic flux is weber.

1 Wb = 1 T m²

The dimensional formula of magnetic flux is:

[ΦB] = [M L² T⁻² A⁻¹]

Faraday’s Law in CBSE Class 12 Physics Chapter 6 Notes

Faraday’s law of electromagnetic induction relates induced emf to the rate of change of magnetic flux.

Faraday’s First Law

Whenever the magnetic flux linked with a circuit changes, an emf is induced in the circuit.

If the circuit is closed, the induced emf produces an induced current.

The emf exists only while the magnetic flux is changing.

Faraday’s Second Law

The magnitude of the induced emf is equal to the rate of change of magnetic flux.

For a single loop:

ε = −dΦB/dt

For a coil with N turns:

ε = −N(dΦB/dt)

The negative sign represents the direction given by Lenz’s law.

Average Induced EMF

If the flux changes from Φ1 to Φ2 in time Δt:

εavg = −N(Φ2 − Φ1)/Δt

Therefore:

εavg = −NΔΦB/Δt

The magnitude is:

|εavg| = N|ΔΦB|/Δt

Induced Current

If the circuit has resistance R:

I = ε/R

The induced current depends on:

• Rate of flux change
• Number of turns
• Circuit resistance

Ways to Change Magnetic Flux

Since:

ΦB = BA cos θ

flux can be changed by changing:

• Magnetic field B
• Surface area A
• Angle θ
• Any combination of these quantities

Factors Increasing Induced EMF

The induced emf becomes larger when:

• Magnetic flux changes faster.
• The coil has more turns.
• The magnetic field is stronger.
• Relative motion is faster.
• A soft-iron core increases the magnetic flux.

Lenz’s Law and Conservation of Energy Revision Notes

Lenz’s law gives the polarity of induced emf and the direction of induced current.

Statement of Lenz’s Law

The induced current flows in a direction that opposes the change in magnetic flux that produces it.

This opposition is represented by the negative sign in:

ε = −N(dΦB/dt)

The induced current opposes the flux change. It does not always oppose the magnetic field itself.

Magnet Approaching a Coil

Suppose the north pole of a magnet moves towards a coil.

The magnetic flux through the coil increases.

The induced current creates a magnetic field that opposes this increase. The face of the coil near the magnet behaves like a north pole and repels the approaching magnet.

Magnet Moving Away from a Coil

When the north pole moves away:

• Magnetic flux through the coil decreases.
• The induced current tries to maintain the original flux.
• The near face of the coil behaves like a south pole.
• The coil attracts the receding north pole.

Finding Induced-Current Direction

Use the following sequence:

1. Identify whether magnetic flux is increasing or decreasing.
2. Determine the direction of the original magnetic field through the loop.
3. Find the direction of the induced magnetic field needed to oppose the change.
4. Apply the right-hand thumb rule to find the induced-current direction.

Lenz’s Law and Conservation of Energy

Lenz’s law follows the law of conservation of energy.

When a magnet is pushed towards a coil:

• The induced current produces a repulsive force.
• External work must be done to move the magnet.
• This mechanical energy changes into electrical energy.
• The electrical energy may be dissipated as heat.

If the induced current supported the motion instead of opposing it, the magnet would accelerate without any energy input. That would violate conservation of energy.

Open and Closed Circuits

In a closed circuit:

• An emf is induced.
• Current flows.

In an open circuit:

• An emf is still induced across the open ends.
• No continuous current flows.

Motional EMF in Class 12 Electromagnetic Induction Revision Notes

A motional emf is produced when a conductor moves through a magnetic field.

Moving Rod in a Magnetic Field

Consider a rod of length l moving with speed v perpendicular to a uniform magnetic field B.

The induced emf is:

ε = Blv

This expression applies when:

• Rod length is perpendicular to velocity.
• Velocity is perpendicular to magnetic field.
• The magnetic field is uniform.

Derivation from Changing Flux

Suppose a moving rod forms one side of a rectangular circuit.

If the enclosed area is:

A = lx

then:

ΦB = Blx

Using Faraday’s law:

ε = −dΦB/dt

ε = −Bl(dx/dt)

For speed v:

|ε| = Blv

Derivation Using Lorentz Force

A charge q in the moving rod experiences magnetic force:

F = q(v × B)

For mutually perpendicular v and B:

F = qvB

Work done in moving charge through the rod length l is:

W = qvBl

Therefore:

ε = W/q

ε = Blv

General Motional EMF

If v makes an angle θ with B:

ε = Blv sin θ

The emf is zero when the conductor moves parallel to the magnetic field.

Current and Magnetic Force

If the total circuit resistance is R:

I = Blv/R

The current-carrying rod experiences a magnetic force:

F = BIl

Substituting I:

F = B²l²v/R

This force opposes the rod’s motion according to Lenz’s law.

Mechanical Power and Electrical Power

Mechanical power supplied is:

Pmechanical = Fv

Using the force expression:

Pmechanical = B²l²v²/R

Electrical power dissipated is:

Pelectrical = I²R

Since I = Blv/R:

Pelectrical = B²l²v²/R

Therefore:

Pmechanical = Pelectrical

This confirms conservation of energy.

Rotating Rod

For a rod of length R rotating with angular speed ω about one end in a perpendicular magnetic field:

ε = ½BωR²

This follows because different parts of the rod move at different linear speeds.

Inductance in Physics Chapter 6 Revision Notes

Inductance describes the ability of a coil or circuit to oppose a change in electric current.

Flux Linkage

For a coil with N turns and magnetic flux ΦB through each turn:

Flux linkage = NΦB

If the coil geometry and magnetic medium remain fixed:

NΦB ∝ I

Therefore:

NΦB = LI

Here, L is the inductance of the coil.

Unit and Dimensions of Inductance

The SI unit of inductance is henry.

1 H = 1 Wb/A

It can also be written as:

1 H = 1 V s/A

The dimensional formula is:

[L] = [M L² T⁻² A⁻²]

Inductance is a scalar quantity.

It depends on:

• Number of turns
• Coil dimensions
• Relative position and orientation
• Core material
• Magnetic permeability

Mutual Inductance in Electromagnetic Induction Revision Notes

Mutual inductance describes the induction of emf in one coil due to a changing current in another nearby coil.

Definition of Mutual Inductance

Consider two nearby coils.

If current I2 in coil 2 produces magnetic flux Φ1 through each turn of coil 1:

N1Φ1 = M12I2

Here, M12 is the mutual inductance of coil 1 with respect to coil 2.

Similarly:

N2Φ2 = M21I1

For a pair of coils:

M12 = M21 = M

Induced EMF Due to Mutual Induction

When current I2 changes:

ε1 = −M(dI2/dt)

Similarly:

ε2 = −M(dI1/dt)

The induced emf becomes larger when:

• Mutual inductance is larger.
• Current changes faster.

Mutual Inductance of Coaxial Solenoids

For two long coaxial solenoids of common length l:

M = μ₀n1n2Al

Here:

• n1 and n2 are turns per unit length.
• A is the common cross-sectional area.
• l is the common length.

If a magnetic core of relative permeability μr is present:

M = μrμ₀n1n2Al

Factors Affecting Mutual Inductance

Mutual inductance depends on:

• Number of turns in each coil
• Shared cross-sectional area
• Coil separation
• Relative orientation
• Core material
• Magnetic permeability

It is maximum when the coils are close and their axes coincide.

Self-Inductance in CBSE Class 12 Electromagnetic Induction Notes

Self-inductance is the property of a coil by which a changing current induces an emf in the same coil.

Self-Induced EMF

For one coil:

NΦB = LI

When current changes:

ε = −L(dI/dt)

The induced emf opposes:

• Increase in current
• Decrease in current

For this reason, self-induced emf is also called back emf.

Electrical Inertia

Self-inductance acts like inertia in mechanics.

• Mass opposes a change in velocity.
• Inductance opposes a change in current.

A larger inductance produces greater opposition to current change.

Self-Inductance of a Long Solenoid

For a long solenoid:

L = μ₀n²Al

Here:

• n is the number of turns per unit length.
• A is cross-sectional area.
• l is the solenoid length.

If the solenoid contains a magnetic material of relative permeability μr:

L = μrμ₀n²Al

Using total turns N = nl:

L = μ₀N²A/l

With a magnetic core:

L = μrμ₀N²A/l

Factors Affecting Self-Inductance

Self-inductance increases when:

• Number of turns increases.
• Cross-sectional area increases.
• Magnetic permeability increases.

It decreases when the solenoid length increases, if the total number of turns remains fixed.

Energy Stored in an Inductor Chapter 6 Physics Notes

Work must be done against the back emf while establishing current in an inductor.

This work is stored as magnetic energy.

Energy Stored in an Inductor

The energy stored in an inductor carrying current I is:

U = ½LI²

Here:

• L is self-inductance.
• I is current.

This formula resembles kinetic energy:

K = ½mv²

The comparison shows:

• L acts like electrical inertia.
• I plays a role similar to velocity.

Magnetic Energy Density

For a long air-core solenoid:

B = μ₀nI

The energy stored is:

U = ½LI²

Using:

L = μ₀n²Al

we get:

U = B²Al/(2μ₀)

Since volume V = Al:

uB = U/V

Therefore:

uB = B²/(2μ₀)

This is the magnetic-energy density in vacuum.

In a linear magnetic medium:

uB = B²/(2μ)

It may also be written as:

uB = ½BH

Electric and Magnetic Energy Comparison

AC Generator in Class 12 Physics Electromagnetic Induction Notes

An AC generator converts mechanical energy into electrical energy using electromagnetic induction.

Principle of an AC Generator

An emf is induced when a coil rotates in a magnetic field because the magnetic flux linked with it changes continuously.

For a coil of N turns and area A rotating in uniform magnetic field B:

ΦB = BA cos θ

If the coil rotates with angular speed ω:

θ = ωt

Therefore:

ΦB = BA cos ωt

For N turns, flux linkage is:

NΦB = NBA cos ωt

Using Faraday’s law:

ε = −d(NΦB)/dt

Therefore:

ε = NBAω sin ωt

Let:

ε0 = NBAω

Then:

ε = ε0 sin ωt

Here, ε0 is the maximum induced emf.

Generator Frequency

Since:

ω = 2πν

the induced emf may be written as:

ε = NBA(2πν) sin(2πνt)

The frequency of the generated emf equals the rotational frequency of the coil.

Main Parts of an AC Generator

An AC generator contains:

• Armature: Rotating coil with N turns
• Magnetic field: Produced by permanent magnets or electromagnets
• Rotor shaft: Rotates the coil
• Slip rings: Connected to the coil ends
• Brushes: Provide contact with the external circuit
• External mechanical source: Rotates the coil

Working of an AC Generator

As the coil rotates:

• Its orientation relative to B changes.
• Magnetic flux changes continuously.
• An alternating emf is induced.
• The emf changes direction after every half rotation.

The emf is:

• Zero when the area vector is parallel to B because flux change is momentarily zero.
• Maximum when the area vector is perpendicular to B because the rate of flux change is maximum.

Flux and EMF Comparison

The magnetic flux and induced emf differ in phase by 90°.

Electromagnetic Induction Formula Notes

Important Terms in Class 12 Physics Chapter 6

Access Class 12 Physics Chapter 6 Electromagnetic Induction Notes in 30 Minutes

Divide the chapter into three revision blocks:

• First 10 minutes: Faraday and Henry experiments, magnetic flux and Faraday’s law
• Next 10 minutes: Lenz’s law, induced-current direction and motional emf
• Final 10 minutes: Mutual inductance, self-inductance, stored energy and AC generator

While solving flux questions, check whether the given angle is with the area vector or the plane. For direction-based questions, first decide whether flux is increasing or decreasing.

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