Electromagnetic Induction — Physics Class 12 Notes (CBSE & HBSE)
Free NCERT Physics notes for Electromagnetic Induction (Class 12) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Electromagnetic Induction (CBSE & HBSE)
CBSE focuses on Faraday's law derivation, Lenz's law, motional EMF calculation, self and mutual inductance derivations, and energy stored in inductor. HBSE emphasizes Faraday's laws statement, Lenz's law, and basic numericals on EMF and inductance.
Faraday's Laws and Lenz's Law
Magnetic Flux
The magnetic flux through a surface is the total number of magnetic field lines passing through it:
φ = B⃗·A⃗ = BA cosθ
where θ = angle between B⃗ and area vector A⃗. Unit: Weber (Wb) = T·m²
For a coil of N turns: φ_total = Nφ (flux linkage)
Faraday's Laws of Electromagnetic Induction
First Law: Whenever the magnetic flux through a circuit changes, an electromotive force (EMF) is induced in the circuit.
Second Law (Quantitative): The magnitude of induced EMF is proportional to the rate of change of magnetic flux:
ε = −N·dφ/dt = −dφ_linkage/dt
The negative sign is from Lenz's law.
Lenz's Law
The induced current always flows in such a direction that its magnetic effect opposes the change in flux that caused it.
- Flux increasing → induced current creates opposing field
- Flux decreasing → induced current creates supporting field
Lenz's law is a consequence of conservation of energy.
Methods to Change Flux
- Change B (move magnet)
- Change area A (deform coil)
- Change θ (rotate coil)
- Change number of turns N (not practical)
Faraday's Law in Integral Form
ε = ∮E⃗·dl⃗ = −dφ_B/dt
This is one of Maxwell's equations — a time-varying B field creates an electric field even in free space.
Induced EMF: Formula Summary
| Change | Formula | Notes |
|---|---|---|
| Moving magnet | ε = −N·Δφ/Δt | Average EMF |
| Rotating coil | ε = NBAω sinωt | AC generator |
| Moving conductor | ε = Blv | Motional EMF |
Diagram Indicator: [Magnet approaching a coil with induced current and arrows showing direction by Lenz's law; also flux vs time graph showing how ε = −dφ/dt relates to slope of φ-t graph.]
Motional EMF and Eddy Currents
Motional EMF
When a conductor of length l moves with velocity v perpendicular to a magnetic field B:
ε = Blv
Derivation: Free electrons in the conductor experience Lorentz force F = qvB. This separates charges, creating potential difference.
For a circuit with resistance R: I = ε/R = Blv/R
Force needed to maintain velocity (energy source): F_app = BIl = B²l²v/R
Power input = Power dissipated: P = F·v = ε·I = ε²/R = B²l²v²/R ✓
AC Generator Principle
A coil of N turns, area A, rotating with ω in field B:
ε = NBAω sinωt = ε₀ sinωt
where ε₀ = NBAω = peak EMF
Eddy Currents
Eddy currents (Foucault currents) are induced currents in bulk conductors (not in discrete wires) due to changing flux.
Production: When a solid conductor moves in B or B changes, EMF is induced → currents flow in closed loops within the metal.
Effects and Applications of Eddy Currents
| Application | How Eddy Currents Help |
|---|---|
| Magnetic braking | Opposing force slows conductor (trains, scales) |
| Induction heating | I²R heating melts metals (induction cooker, furnace) |
| Metal detectors | Change in eddy current pattern detects metal |
| Speedometers | Eddy current drag is proportional to speed |
Reducing Eddy Currents:
- Use laminated cores (thin sheets of iron insulated from each other)
- Sheets ⊥ to the induced EMF path → reduce current loop area → reduce I → reduce I²R loss
Energy Conservation in EMI
Work done by external agent → kinetic energy of conductor → electrical energy → heat in resistance
At all stages, energy is conserved. Lenz's law ensures this.
Diagram Indicator: [Conductor of length l moving right with velocity v in magnetic field B (into page); force on +ve charges upward; EMF=Blv; also eddy current loops in a solid metal plate moving in field B.]
Mutual and Self Induction
Self Induction
When current through a coil changes, the changing flux induces an EMF in the same coil that opposes the change in current.
ε_self = −L·dI/dt
where L = self-inductance (Henry, H)
L = Nφ/I = N²μ₀A/l (for solenoid of length l, N turns, area A)
Self-inductance of solenoid: L = μ₀n²V = μ₀n²Al where n = N/l = turns per unit length, V = volume
Energy Stored in Inductor
U = ½LI²
This energy is stored in the magnetic field.
Magnetic energy density: u = B²/(2μ₀) = ½μ₀H²
Mutual Induction
When current in one coil (primary) changes, the changing flux through the second coil (secondary) induces an EMF in it.
ε_secondary = −M·dI_primary/dt
where M = mutual inductance (Henry, H)
M = N₂φ₂/I₁ = N₁φ₁/I₂ (from reciprocity)
For two coaxial solenoids: M = μ₀N₁N₂A/l
Coupling coefficient: k = M/√(L₁L₂), 0 ≤ k ≤ 1
Transformer (Based on Mutual Induction)
Turns ratio: N_s/N_p = V_s/V_p = I_p/I_s
Step-up: N_s > N_p → V_s > V_p Step-down: N_s < N_p → V_s < V_p
Efficiency: η = P_s/P_p = V_s I_s/(V_p I_p) × 100%
Ideal transformer: V_s I_s = V_p I_p (100% efficiency)
Comparison: Self vs Mutual Inductance
| Property | Self Inductance L | Mutual Inductance M |
|---|---|---|
| Coils involved | 1 coil | 2 coils |
| EMF induced | In same coil | In secondary coil |
| Formula | ε = −L dI/dt | ε = −M dI/dt |
| Energy | ½LI² (stored) | Couples energy between coils |
Diagram Indicator: [Two coaxial solenoids showing magnetic flux linkage for mutual inductance; also single solenoid showing self-inductance with flux lines through it; transformer with primary and secondary windings labeled.]
Frequently asked questions
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Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Electromagnetic Induction.