Electromagnetic Induction Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 6 notes: magnetic flux, Faraday's laws, Lenz's law, motional EMF, eddy currents, self and mutual inductance and energy stored.
Electromagnetic Induction — Class 12 Physics Notes
Chapter Snapshot
A changing magnetic flux produces an EMF — that single discovery (Faraday) underlies generators, transformers, and induction motors. This chapter covers magnetic flux, Faraday's laws, Lenz's law, motional EMF, eddy currents, and inductance (self and mutual) with the energy stored in an inductor.
Board relevance: the EMI + AC unit is ~8 marks. Expect a Faraday/Lenz reasoning question and an inductance or motional-EMF numerical. The minus sign in Faraday's law is worth marks — it is Lenz's law.
Key Concepts & Definitions
Magnetic flux (Φ) — the amount of magnetic field passing through a surface:
Φ = B·A = BA cos θ (unit: weber, Wb; a scalar)
θ is the angle between B and the area vector (the normal to the surface). Flux is maximum when B is perpendicular to the surface (θ = 0) and zero when B lies in the plane (θ = 90°).
Faraday's laws of induction:
1. An EMF is induced whenever the magnetic flux linked with a circuit changes.
2. The induced EMF equals the negative rate of change of flux:
ε = −dΦ/dt, and for a coil of N turns ε = −N dΦ/dt
Flux can change by changing B, the area A, or the orientation θ.
Lenz's law — the induced current flows so as to oppose the change that produced it. This is the meaning of the minus sign, and it follows from conservation of energy: if the induced current aided the change, energy would be created from nothing.
Example: pushing a magnet's north pole towards a coil induces a current making the near face a north pole (repelling it); pulling it away induces the opposite current (attracting it). Either way you must do work — that work becomes the electrical energy.
Motional EMF and Eddy Currents
Motional EMF — a rod of length l moving with velocity v perpendicular to a field B:
ε = Blv
If the rod slides on rails of resistance R, the induced current is I = Blv/R, the force opposing the motion is F = B²l²v/R, and the power dissipated is P = B²l²v²/R (equal to the mechanical power you supply).
Eddy currents — circulating induced currents set up in the body of a bulk conductor when the flux through it changes. They dissipate energy as heat, so transformer and motor cores are laminated (thin insulated sheets) to break up the current paths. Useful applications: electromagnetic braking in trains, induction furnaces, and analogue speedometers.
Formulas — Inductance
Self-inductance (L) — a coil opposes changes in its own current:
ε = −L dI/dt ; Φ = LI (unit: henry, H)
For a long solenoid: L = μ₀n²Al (n = turns per metre, A = area, l = length), or L = μ₀N²A/l.
Mutual inductance (M) — a changing current in coil 1 induces an EMF in coil 2:
ε₂ = −M dI₁/dt ; Φ₂ = MI₁
For two coaxial solenoids, M = μ₀n₁n₂Al. Mutual inductance is the principle behind the transformer.
Energy stored in an inductor:
U = ½LI²
(analogous to ½CV² for a capacitor — the energy is stored in the magnetic field).
Worked Examples
Example 1 — Faraday's law: The flux through a 200-turn coil changes from 0.05 Wb to 0.01 Wb in 0.2 s. Find the induced EMF.
ε = −N ΔΦ/Δt = −200 × (0.01 − 0.05)/0.2 = −200 × (−0.2) = 40 V (magnitude).
Example 2 — Motional EMF: A 0.5 m rod moves at 4 m/s perpendicular to a 0.2 T field. Find the EMF.
ε = Blv = 0.2 × 0.5 × 4 = 0.4 V.
Example 3 — Self-inductance: A current of 2 A in a coil falls to zero in 0.1 s, inducing 40 V. Find L.
ε = L dI/dt → 40 = L × (2/0.1) = 20L → L = 2 H.
Example 4 — Energy stored: Find the energy in a 2 H inductor carrying 3 A.
U = ½LI² = ½ × 2 × 9 = 9 J.
Important Question Patterns
1. Faraday/Lenz (2–3 marks): find the induced EMF from a flux change; state and apply Lenz's law; direction of the induced current in a given figure.
2. Motional EMF (3 marks): ε = Blv; the current, retarding force, and power in a rod-on-rails setup.
3. Inductance (2–3 marks): define self/mutual inductance; L of a solenoid; EMF from dI/dt.
4. Energy (2 marks): U = ½LI²; compare with a capacitor's ½CV².
5. Eddy currents (2 marks): what they are, why cores are laminated, and their applications.
⚡ Quick Revision
- Flux Φ = BA cos θ (weber, scalar); changes via B, A, or θ.
- Faraday: ε = −N dΦ/dt. The minus sign is Lenz's law.
- Lenz's law: induced current opposes the change; follows from conservation of energy.
- Motional EMF ε = Blv; I = Blv/R, retarding force F = B²l²v/R.
- Eddy currents: heat losses → laminated cores; used in braking, induction furnaces, speedometers.
- Self-inductance: ε = −L dI/dt, Φ = LI, solenoid L = μ₀n²Al (henry).
- Mutual inductance: ε₂ = −M dI₁/dt — basis of the transformer.
- Energy U = ½LI² (magnetic analogue of ½CV²).
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