Physics Electromagnetic Induction Class 12 Notes by PW

Electromagnetic induction explains the relationship between magnetism and electricity. It describes how a changing magnetic field, area or orientation can produce an electromotive force (EMF). Questions often test magnetic flux, the direction of induced current, Faraday’s and Lenz’s laws, motional EMF and the difference between self-induction and mutual induction.

Physics Wallah offers Electromagnetic Induction Class 12 notes to help you understand these concepts, learn important formulas and solve numerical problems. Use these notes to revise the applications of electromagnetic induction, understand the working of inductors and prepare effectively for your Class 12 Physics examinations.

Magnetic Flux

Magnetic flux measures the magnetic field passing through a given surface. It depends on the magnetic field, the area of the surface and its orientation.

The area vector is perpendicular to the plane of the surface. The angle θ in the formula is measured between the magnetic field vector and the area vector.

For a uniform magnetic field:

Φ_B = B A cos θ

Where:

• B = Magnetic field

• A = Area of the surface

• θ = Angle between the magnetic field and the area vector

In vector form:

Φ_B = B · A (dot product of B and A)

Special Cases of Magnetic Flux

• When θ = 0°: Magnetic flux is maximum, Φ_B = BA.

• When θ = 90°: Magnetic flux is zero, Φ_B = 0.

When the magnetic field lies in the plane of the surface, the area vector is perpendicular to the magnetic field, making the flux zero.

• Magnetic flux is a scalar quantity.

• SI unit: Weber (Wb)

• CGS unit: Maxwell (Mx)

• 1 Wb = 1 T m²

Magnetic Flux in a Non-Uniform Field

When the magnetic field varies across the surface, divide the surface into small area elements. The flux through a small area element is:

dΦ_B = B · dA

The total magnetic flux is:

Φ_B = ∫ B · dA

Memory Tip: In BA cos θ, remember that the angle is between the magnetic field and the area vector, not the plane of the surface.

Electromagnetic Induction

Electromagnetic induction is the phenomenon in which an EMF is produced due to a change in magnetic flux linked with a circuit.

• If the circuit is closed, the induced EMF produces current.

• If the circuit is open, EMF can still exist, but current does not flow.

How Can Magnetic Flux Change?

• Moving a magnet towards or away from a coil.

• Changing the magnetic field around a coil.

• Changing the area of the coil.

• Rotating the coil in a magnetic field.

Important: Induced EMF and current exist only while the magnetic flux is changing. When the flux becomes constant, the induced EMF becomes zero.

Faraday’s Laws of Electromagnetic Induction

Faraday established two important laws:

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

2. The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux.

For a finite change in magnetic flux:

ε = − ΔΦ_B / Δt

For continuous change:

ε = − dΦ_B / dt

For a coil having N turns:

ε = − N (dΦ_B / dt)

A faster change in magnetic flux produces a greater induced EMF.

Memory Tip: Changing flux produces EMF. A closed circuit allows induced current to flow. Constant flux produces no induced EMF.

Lenz’s Law

Lenz’s law determines the direction of the induced current. It states that the induced current flows in a direction that opposes the change in magnetic flux responsible for producing it.

• When magnetic flux increases, the induced current tries to decrease it.

• When magnetic flux decreases, the induced current tries to increase it.

• The induced current opposes the change in magnetic flux, not necessarily the magnetic field itself.

• The negative sign in Faraday’s law represents this opposition.

Magnetic Poles in a Coil

• North pole approaches: the near face of the coil becomes North, causing repulsion.

• North pole moves away: the near face of the coil becomes South, causing attraction.

• South pole approaches: the near face of the coil becomes South, causing repulsion.

• South pole moves away: the near face of the coil becomes North, causing attraction.

The coil always opposes the change caused by the moving magnet.

Clock-Face Rule

When you observe a coil from a particular side:

• Clockwise current → South pole

• Anticlockwise current → North pole

Always specify the side from which you are observing the coil. Observers on opposite sides may see opposite current directions.

Memory Tip: Clockwise = South; Anticlockwise = North.

Motional EMF

When a conductor moves through a magnetic field, the magnetic flux linked with the circuit may change, producing an EMF. This is called motional EMF.

Consider a conducting rod of length L moving with velocity v perpendicular to a uniform magnetic field B. The induced EMF is:

ε = B L v

If the resistance of the circuit is R, the induced current is:

I = B L v / R

Motional EMF depends on the magnetic field, length of the conductor and its velocity. Resistance affects the current, not the EMF.

Fleming’s Right-Hand Rule

Use this rule to determine the direction of induced current:

• First finger: Magnetic field

• Thumb: Motion of conductor

• Middle finger: Induced current

Memory Tip: Field → First finger; Motion → Thumb; Current → Middle finger.

Rotating Rod and Alternating EMF

Consider a conducting rod of length L rotating with angular velocity ω in a uniform magnetic field B. The EMF induced between its ends is:

ε = B ω L² / 2

If the rod has resistance R:

I = B ω L² / (2R)

The heat produced in time t is:

H = B² ω² L⁴ t / (4R)

EMF Produced by a Rotating Coil

For a coil having N turns and area A, rotating with angular velocity ω in a magnetic field B:

• Maximum EMF: ε₀ = N B A ω

• Instantaneous EMF: ε = ε₀ sin ωt

The EMF changes periodically between positive and negative maximum values. This is called alternating EMF, and the corresponding current is called alternating current (AC).

Eddy Currents

When a conducting block or sheet is placed in a changing magnetic field, circulating currents are induced within the conductor. These are called eddy currents, also known as whirlpool currents or Foucault currents.

Characteristics of Eddy Currents

• They oppose the change in magnetic flux responsible for their production.

• They produce heat in the conductor.

• They may cause unwanted energy loss.

Applications of Eddy Currents

• Induction furnaces for heating metals.

• Electromagnetic damping in instruments.

• Electric brakes.

• Speedometers.

• Induction meters.

• Electromagnetic shielding.

How Can Eddy Current Losses Be Reduced?

Eddy current losses can be reduced by laminating the conducting material into thin sheets or applying suitable coatings. This restricts the circulation of eddy currents and reduces energy loss.

Self-Induction

Self-induction is the phenomenon in which a changing current in a coil produces an induced EMF in the same coil.

When current changes, the magnetic field and magnetic flux linked with the coil also change. This produces an EMF that opposes the change in current.

The self-induced EMF is:

ε = − L (dI/dt)

Here, L is the self-inductance of the coil. The self-induced EMF is also called back EMF.

The flux linkage is related to current by:

N Φ_B = L I

Self-induced EMF exists only when the current changes. When the current becomes constant, the self-induced EMF becomes zero.

Self-Inductance of a Long Solenoid

L = μ N² A / l

Where:

• L = Self-inductance

• μ = Permeability of the medium

• N = Number of turns

• A = Cross-sectional area

• l = Length of the solenoid

Factors Affecting Self-Inductance

Self-inductance increases when:

• The number of turns increases.

• The cross-sectional area increases.

• The length of the solenoid decreases.

• A soft-iron core is inserted.

An iron-core solenoid has greater inductance than an air-core solenoid because of its higher permeability.

Energy Stored in an Inductor

An inductor stores energy in its magnetic field.

U = ½ L I²

Where L is inductance and I is the current flowing through it.

Mutual Induction

Mutual induction occurs when a changing current in one coil produces an induced EMF in another nearby coil.

Consider two coils:

• Primary coil: Connected to a source of current.

• Secondary coil: Placed near the primary coil.

When current in the primary changes, its magnetic field changes. This changes the magnetic flux linked with the secondary coil, producing an induced EMF:

ε₂ = − M (dI₁/dt)

Here, M is the mutual inductance of the two coils.

Mutual Inductance of Two Long Coaxial Solenoids

M = μ N₁ N₂ A / l₁

Where:

• N₁ = Number of turns in the primary

• N₂ = Number of turns in the secondary

• A = Cross-sectional area of the secondary coil

• l₁ = Length of the primary solenoid

Coefficient of Coupling

The coefficient of coupling tells us how effectively the magnetic flux of one coil links with the other.

K = M / √(L₁ L₂)

Its value lies between 0 and 1.

• K = 0: No magnetic coupling.

• K = 1: Perfect magnetic coupling.

Equivalent Inductance of Coupled Coils in Series

• Series aiding: L_eq = L₁ + L₂ + 2M

• Series opposing: L_eq = L₁ + L₂ − 2M

The sign of mutual inductance depends on whether the magnetic fields produced by the two coils aid or oppose each other.

Electromagnetic induction explains how changing magnetic flux produces EMF and current. Faraday’s law determines the magnitude of induced EMF, while Lenz’s law determines its direction. Motional EMF, eddy currents, self-induction and mutual induction show how this principle works in conductors and coils. Revise the important formulas, understand the direction of induced current and practise numerical questions to strengthen your preparation for Class 12 Physics. Physics Wallah notes and NCERT questions can help you revise the chapter and prepare for board examinations.