Chapter 6 — Electromagnetic Induction
A changing magnetic flux drives an emf around any loop it threads — the discovery behind every generator, transformer, wireless charger and guitar pickup.
Almost every unit of electrical energy you have ever used was made by moving a magnet past a coil of wire, or a coil past a magnet. In a hydroelectric station on the Bhakra dam or a coal-fired plant near Singrauli, a turbine spins a huge electromagnet inside a ring of copper windings fifty times a second, and the voltage that appears in the windings travels across the grid to your wall socket. The same effect, in miniature, charges a phone that is simply laid on a charging pad, reads the magnetic strip of a bank card, picks up the vibration of an electric-guitar string and switches traffic lights when a car stops over a buried loop of wire.
In 1831 Michael Faraday in London (and, independently, Joseph Henry in the United States) found the rule behind all of this: an emf appears in a circuit whenever the magnetic flux through it changes — and only then. A magnet resting inside a coil does nothing; the same magnet moving in or out drives a current. This chapter makes that rule quantitative (Faraday's law), finds the direction of the induced current from energy conservation (Lenz's law), explains the emf of a conductor moving through a field from the magnetic force on its charges, and introduces inductance — the way coils link flux with themselves and with each other — before putting it all together in the AC generator.
- describe the experiments of Faraday and Henry and say exactly what makes an induced emf appear;
- calculate the magnetic flux through a plane coil at any angle to a uniform field, and the flux linkage of a coil of $N$ turns;
- use Faraday's law $\varepsilon=-N\,d\Phi_B/dt$ for average and instantaneous emfs, and find the charge that flows, $Q=N\Delta\Phi_B/R$;
- find the direction of an induced current with Lenz's law, and explain why the law is a statement of energy conservation;
- derive the motional emf $Blv$ and $\tfrac12B\omega l^2$, and follow the energy from the agent that moves the conductor to the heat in the circuit;
- define and calculate mutual and self-inductance, use $\varepsilon=-L\,dI/dt$ and the energy $\tfrac12LI^2$, and derive the emf $NBA\omega\sin\omega t$ of an AC generator;
- solve board, JEE Main, JEE Advanced and NEET problems on all of the above.
Sections in this chapter
Magnetic Flux, Faraday's Law and Lenz's Law
The experiments of Faraday and Henry, magnetic flux and the weber, Faraday's law of induction, induced charge, and the direction of the induced current from Lenz's law.
Motional EMF and Energy Considerations
The emf of a rod moving through a field, rotating rods and discs, the braking force, terminal velocity, and where the energy goes.
Self and Mutual Inductance and the AC Generator
Mutual inductance of two coils, self-inductance and back emf, the energy stored in an inductor, and the emf of a coil rotating in a field.