CBSE Class 12 › Unit IV: Electromagnetic Induction

Electromagnetic Induction

NCERT Chapter 6 • Faraday’s Law, Lenz’s Law & Inductance

NCERT 2025–26 Unit IV • ~8 Marks JEE Main • 2 Questions

1. Magnetic Flux

Magnetic flux is a measure of the number of magnetic field lines passing through a surface. It is analogous to electric flux.

\Phi_B = \vec{B} \cdot \vec{A} = BA \cos \theta

Unit: Weber (Wb) or Tesla-meter² (Tm²)

2. Faraday’s Law of Induction

Michael Faraday discovered that a changing magnetic flux through a circuit induces an electromotive force (EMF).

\varepsilon = - \frac{d\Phi_B}{dt}

Magnitude: $\varepsilon = N \frac{d\Phi}{dt}$ (for N turns)

Lenz’s Law

The polarity of the induced EMF is such that it tends to produce a current which opposes the change in magnetic flux that produced it.

Conservation of Energy:
Lenz’s Law is a consequence of the law of conservation of energy. Mechanical work done in moving the magnet against the repulsive force is converted into electrical energy (induced current).

3. Motional Electromotive Force

When a conductor moves in a magnetic field, the Lorentz force on charge carriers causes charge separation, creating an EMF.

Setup for deriving motional electromotive force using a sliding conductor on rails. — Rod PQ moving with velocity v in magnetic field B.

Derivation: Motional EMF 3 Marks

Step 1: Magnetic Flux
Consider a loop with a movable arm PQ of length $l$ at position $x$ .
Area $A = lx$ . Flux $\Phi_B = Blx$ .

Step 2: Rate of Change
As the rod moves with speed $v = -dx/dt$ (since x decreases), the flux changes.
$\frac{d\Phi_B}{dt} = \frac{d}{dt}(Blx) = Bl \frac{dx}{dt} = -Blv$ .

Step 3: Induced EMF
Using Faraday’s Law: $\varepsilon = - \frac{d\Phi_B}{dt} = -(-Blv)$ .
$\varepsilon = Blv$ .

4. Eddy Currents

When bulk pieces of conductors are subjected to changing magnetic flux, induced currents flow in closed loops within the conductor, resembling eddies in water.

Illustration of circulating eddy currents formed in a metal plate moving through a magnetic field. — Eddy currents oppose the motion, causing electromagnetic damping.

Applications:

Magnetic Braking in trains.
Induction Furnace (Heat generated by eddy currents melts metal).
Electric Power Meters.

5. Inductance

Electric current produces a magnetic field. If the current changes, the field changes, inducing an EMF. This phenomenon is Inductance.

A. Mutual Inductance

The phenomenon where a changing current in one coil induces an EMF in a neighboring coil.

Diagram of two coaxial solenoids used to derive mutual inductance.

Derivation: Mutual Inductance of Coaxial Solenoids 3 Marks

Step 1: Field Calculation
Current $I_2$ in outer solenoid $S_2$ produces field $B_2 = \mu_0 n_2 I_2$ .

Step 2: Flux through Inner Coil
Flux through one turn of $S_1$ is $B_2 A_1$ . Total flux $\Phi_1 = N_1 (B_2 A_1)$ .
$\Phi_1 = (n_1 l)(\mu_0 n_2 I_2)(\pi r_1^2)$ .

Step 3: Coefficient M
Since $\Phi_1 = M_{12} I_2$ , we have:
$M = \mu_0 n_1 n_2 \pi r_1^2 l$ .

B. Self Inductance

The phenomenon where a changing current in a coil induces a “back EMF” in the same coil.

Derivation setup for self-inductance showing flux linkage in a long solenoid. — The changing current in the solenoid changes the flux linked with itself.

Derivation: Self Inductance of Long Solenoid 3 Marks

Step 1: Magnetic Field
Consider a long solenoid of length $l$ and area $A$ , with $n$ turns per unit length.
Current $I$ produces a field inside: $B = \mu_0 n I$ .

Step 2: Magnetic Flux
The flux through one turn is $\phi = B \cdot A = (\mu_0 n I) A$ .
Total number of turns $N = n \times l$ .

Step 3: Total Flux Linkage
Total flux $\Phi = N \times \phi = (nl) \times (\mu_0 n I A)$ .
$\Phi = \mu_0 n^2 A l I$ .

Step 4: Coefficient of Self Induction (L)
By definition, $\Phi = L I$ . Comparing this with the result above:
$L = \mu_0 n^2 A l$ .

\varepsilon = -L \frac{dI}{dt}

Magnetic Energy Stored: $U = \frac{1}{2} L I^2$

6. AC Generator

A device that converts mechanical energy into electrical energy based on electromagnetic induction.

Construction diagram and working principle of an AC Generator. — As the coil rotates, the angle $\theta$ changes, changing the flux.

Principle:
Flux $\Phi_B = NBA \cos(\omega t)$ .
Induced EMF $\varepsilon = - \frac{d\Phi}{dt} = -NBA \frac{d}{dt}(\cos \omega t)$ .
$\varepsilon = NBA\omega \sin(\omega t)$ .

This produces an alternating voltage with maximum value $\varepsilon_0 = NBA\omega$ .

Practice Time!
Ready to test your knowledge? Try 10 solved numericals on EMI: Click here →

← Previous: Magnetism & Matter Next: Alternating Current →