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Class 12 · Physics

Electromagnetic Induction

A compass needle moves when a current flows nearby. A light bulb flickers when a transformer is switched on.

Feynman Lens

Start with the simplest version: this lesson is about Electromagnetic Induction. If you can explain the core idea to a friend using everyday language, examples, and one clear reason why it matters, you have moved from memorising to understanding.

A compass needle moves when a current flows nearby. A light bulb flickers when a transformer is switched on. These phenomena reveal the converse of moving-charges-and-magnetism: a changing magnetic field generates an electric field. This reciprocal relationship—electricity generating magnetism and magnetism generating electricity—is the foundation of generators, transformers, and wireless power transfer. It's the deep symmetry that unified electricity and magnetism into electromagnetism.

Faraday's Discovery

Michael Faraday observed that moving a magnet near a coil of wire induces an electric current—even without touching the wire. The changing magnetic field through the coil creates a voltage. This was revolutionary: magnetism could create electricity.

Electromagnetic induction is the production of an electric field (or EMF) by a changing magnetic flux.

Magnetic Flux

Magnetic flux (Φ) measures how much magnetic field passes through a surface:

Φ = BA cos(θ)

Where:

Flux is measured in webers (Wb). Think of it as counting magnetic field lines—more field lines passing through = greater flux.

Faraday's Law of Induction

The induced EMF in a loop is proportional to the rate of change of magnetic flux:

EMF = -N(dΦ/dt)

Where N is the number of turns in the coil. The negative sign (Lenz's law) indicates that the induced EMF opposes the change causing it.

This is profound: a changing magnetic field creates an electric field. No charges needed—the field itself generates the effect.

Lenz's Law

The induced current flows in a direction that opposes the change in magnetic flux. If flux through a coil increases, the induced current creates a magnetic field opposing this increase. If flux decreases, the induced current tries to maintain it.

Example: Push a magnet into a coil. The induced current creates a magnetic field repelling the magnet—making it harder to push. Remove the magnet, and the induced current tries to hold it back. Nature resists change.

This explains why moving through a magnetic field feels like pushing through resistance—the induced effects oppose your motion.

Motional EMF

When a conductor moves through a magnetic field, charges inside experience a Lorentz force, separating positive and negative charges—creating a potential difference:

EMF = BLv

Where:

This is how a generator works: rotate a coil in a magnetic field, and charges are continuously separated, creating AC voltage.

Transformers

A transformer has two coils (primary and secondary) wound around an iron core. AC current in the primary coil creates a changing magnetic field, which induces voltage in the secondary coil.

V_s/V_p = N_s/N_p

Where N is the number of turns. This lets you step voltage up or down. High voltage transmission over long distances, then step down at homes.

Key principle: Power is approximately conserved (ideal transformer): V_p I_p ≈ V_s I_s

Step up voltage → step down current (less power loss in wires, which goes as I²R).

Self-Induction and Inductance

When current in a coil changes, the changing magnetic field it creates induces a back-EMF that opposes the change. This self-inductance (L) is measured in henries (H).

V = -L(dI/dt)

Higher inductance means the coil "resists" current changes more strongly. An iron core dramatically increases inductance because iron amplifies the magnetic field.

moving-charges-and-magnetism | magnetism-and-matter | alternating-current | electromagnetic-waves

Socratic Questions

  1. Why must the magnetic flux through a coil be changing for an EMF to be induced? Why doesn't a constant magnetic field (even a strong one) cause current to flow?
  1. According to Lenz's law, nature opposes changes in magnetic flux. Does this violate conservation of energy? Where does the energy for this opposition come from?
  1. In a transformer, energy transfers from primary to secondary coil through the changing magnetic field, yet the coils never physically touch. How does nature accomplish this "wireless" power transfer?
  1. AC current oscillates between positive and negative, yet a transformer can step up voltage. How is energy conserved when current decreases but voltage increases?
  1. Why do induction cooktops use alternating magnetic fields rather than static magnetic fields? What property of AC fields is essential for this application?
🃏 Flashcards — Quick Recall
Quantity
Magnetic flux (Φ)
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Φ = ∫ B·dA = BA cos θ for uniform B; SI unit weber (Wb) = T·m².
Law
Faraday's Law of Induction
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ε = −dΦ/dt; an EMF is induced by any change in magnetic flux through a circuit.
Law
Lenz's Law
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Induced current direction opposes the change in flux that produced it; consequence of energy conservation.
Formula
Motional EMF
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ε = BLv for a rod of length L moving with speed v perpendicular to a field B.
Quantity
Self-inductance (L)
tap to flip
Φ = LI; back-EMF ε = −L(dI/dt). SI unit henry (H) = V·s/A.
Quantity
Mutual inductance (M)
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EMF in coil 2 from changing current in coil 1: ε₂ = −M(dI₁/dt); M is symmetric (M₁₂ = M₂₁).
Formula
Energy stored in an inductor
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U = ½ L I² — energy is held in the magnetic field around the coil.
Formula
Inductance of a long solenoid
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L = μ₀ n² A ℓ, where n is turns/length, A is cross-section, ℓ is length.
Concept
Eddy currents
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Circulating currents induced in bulk conductors by changing flux; cause dissipation, used for braking.
Device
Ideal transformer relation
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V_s/V_p = N_s/N_p and V_p I_p = V_s I_s; uses mutual induction in a laminated iron core.
📝 Quick Quiz — Test Yourself
A coil of 100 turns has its flux change from 0.02 Wb to 0.05 Wb in 0.1 s. The induced EMF is:
  • A 0.3 V
  • B 3 V
  • C 30 V
  • D 300 V
A rod of length 0.5 m moves at 4 m/s perpendicular to a 0.2 T field. The motional EMF is:
  • A 0.2 V
  • B 0.4 V
  • C 1.0 V
  • D 2.0 V
A bar magnet is pushed north-pole-first toward a coil. The induced current in the coil, viewed from the magnet:
  • A Flows clockwise so the coil attracts the magnet
  • B Is zero because the magnet's field is constant in magnitude
  • C Flows in the same direction as in the magnet
  • D Flows counterclockwise so the coil's near face becomes a north pole repelling the magnet
A 2 H inductor carries 3 A. Energy stored is:
  • A 3 J
  • B 6 J
  • C 9 J
  • D 18 J
An ideal step-up transformer has N_p = 100, N_s = 1000. If primary voltage is 220 V, secondary voltage is:
  • A 2200 V
  • B 22 V
  • C 220 V
  • D 22000 V