Electromagnetic induction, inductance and generators
A changing magnetic flux produces an electric field and an emf. This principle links motion, circuits and mechanical-to-electrical energy conversion.
Flux and Faraday law
For a uniform field through a flat loop, magnetic flux is Φ=BA cosθ, where θ is between B and the area normal. For N turns, ε=−N dΦ/dt. Emf can arise because B, loop area or orientation changes. The minus sign is Lenz law: induced current creates a field opposing the change in flux, preserving energy rather than opposing the existing flux itself.
Motional emf and inductance
A rod of length l moving at speed v perpendicular to B develops ε=Blv. Magnetic forces separate charge until an electric field balances them. A changing current in a coil changes its own flux linkage and produces self-induced emf εL=−L dI/dt. An inductor stores magnetic energy U=½LI² and resists abrupt current change, not current itself.