Electromagnetic Induction
Easy Overview
Remember how moving charges create magnetic fields? Well, it works the other way too — changing magnetic fields create electricity. That's electromagnetic induction. It's the reason generators work, transformers hum, and induction cooktops heat your food without any flame. This chapter is about the beautiful dance between electricity and magnetism.
Faraday's Law
Faraday discovered that a changing magnetic field induces a voltage in a nearby conductor. Move a magnet into a coil of wire — you get a voltage. Move it out — you get a voltage in the opposite direction. The faster you move it, the bigger the voltage. The more turns in the coil, the bigger the voltage. Faraday's law says the induced voltage equals the rate of change of magnetic flux. Flux is just the amount of magnetic field passing through the coil. Change the field, change the area, or change the angle — any of these creates an induced voltage.
Lenz's Law
Lenz's law tells you which way the induced current flows. It always flows in a direction that opposes the change that caused it. If a magnet approaches a coil, the induced current creates a magnetic field that pushes the magnet away. If the magnet moves away, the induced current tries to pull it back. It's like a stubborn friend — whatever you try to do, they resist. Lenz's law is really just the law of conservation of energy in disguise. If the induced current helped the change, you'd get energy from nowhere, which isn't possible.
Self and Mutual Inductance
Self-inductance is when a changing current in a coil induces a voltage in the same coil. The coil basically fights its own current changes — it's called 'back emf.' That's why you can't change the current through an inductor instantly — the inductor resists. Mutual inductance is when a changing current in one coil induces a voltage in a nearby coil. That's how a transformer works — AC current in the primary coil creates a changing magnetic field that induces a voltage in the secondary coil. The voltage can be stepped up or down just by changing the number of turns.
Eddy Currents
Eddy currents are loops of induced current that flow inside a bulk piece of metal exposed to a changing magnetic field. They're like tiny whirlpools of electricity. They cause heating — that's how induction cooktops work (the pan itself becomes the heating element). They also cause braking — some trains use eddy current brakes, where magnets induce currents in the metal wheels, and the interaction slows the train without contact. But eddy currents also waste energy in transformers. That's why transformer cores are laminated — thin sheets with insulation between them break up the eddy current paths and reduce losses.
Key Points
- •Faraday's law: |ε| = dΦ/dt. The induced emf equals the rate of change of magnetic flux.
- •Lenz's law: Induced current opposes the change causing it. It's conservation of energy.
- •Magnetic flux Φ = BA cosθ. B = magnetic field, A = area, θ = angle between B and normal.
- •Self-inductance L: ε = -L di/dt. An inductor stores energy: U = ½LI².
- •Mutual inductance M: ε₂ = -M di₁/dt. Used in transformers.
- •Eddy currents are induced current loops in bulk metal. Minimized by laminating transformer cores.
Practice Questions
- State and explain Faraday's laws of electromagnetic induction. Derive the expression for induced emf.
- State Lenz's law. Show that it is consistent with the law of conservation of energy.
- Describe the working principle of an AC generator (alternator) with a neat diagram.
- A coil of self-inductance 5 H carries a current of 2 A. Find the energy stored in the magnetic field.