⚡ Physics — Class XII

Electromagnetic Induction

How changing magnetic fields create electric currents — Faraday's discovery that powers our world

📖 Chapter 6 ⏱ ~55 min read 🏷️ Electromagnetism

Table of Contents

  1. Introduction
  2. Magnetic Flux
  3. Faraday's Laws of Electromagnetic Induction
  4. Lenz's Law
  5. Motional EMF
  6. Eddy Currents
  7. Self Inductance
  8. Mutual Inductance

6.1 Introduction

Electricity and magnetism were considered separate and unrelated phenomena for a long time. In the early decades of the nineteenth century, experiments by Oersted, Ampere and others established that moving electric charges produce magnetic fields. This naturally raises the question: Is the converse effect possible? Can moving magnets produce electric currents?

6.2 Magnetic Flux

Magnetic flux through a surface is the number of magnetic field lines passing through it:

Φ_B = B · A = BA cos θ
θ is angle between B and the normal to the surface. SI unit: Weber (Wb). 1 Wb = 1 T·m².

6.3 Faraday's Laws of Electromagnetic Induction

Michael Faraday's experiments led to two fundamental laws:

Electromagnetic induction
Figure 6.1 — Faraday's law, Lenz's law, and applications of electromagnetic induction
ε = −dΦ_B/dt
For N turns: ε = −N(dΦ_B/dt). The negative sign represents Lenz's law.

6.4 Lenz's Law

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. This is essentially a consequence of conservation of energy.

💡 Energy Conservation

If the induced current aided the change instead of opposing it, we would get infinite energy from nothing — violating conservation of energy. Lenz's law ensures energy is always conserved.

6.5 Motional EMF

A conductor moving in a magnetic field develops an emf across its ends due to the Lorentz force on free charges:

ε = Blv
B = magnetic field, l = length of conductor, v = velocity perpendicular to both B and l.
⚡ Rotating Rod

For a rod of length l rotating with angular velocity ω about one end in a perpendicular B: ε = ½Bωl². This is the principle behind generators.

6.6 Eddy Currents

When a bulk conductor moves in a magnetic field or the magnetic flux through it changes, circulating currents called eddy currents are induced within the conductor.

6.7 Self Inductance

Self inductance is the property of a coil by which a change in current through it induces an emf in the same coil:

L = NΦ/I or ε = −L(dI/dt)
For a solenoid: L = μ₀n²Al. Energy stored: U = ½LI². SI unit: Henry (H).

6.8 Mutual Inductance

Mutual inductance is the property of two coils by which a change in current in one coil induces an emf in the other coil:

M = N₂Φ₂₁/I₁ or ε₂ = −M(dI₁/dt)
For two coaxial solenoids: M = μ₀n₁n₂A₂l₂. By reciprocity: M₁₂ = M₂₁.
Ch 5 — Magnetism and Matter Ch 7 — Alternating Current

Physics Class XII — Chapter 6: Electromagnetic Induction

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