Faraday's Law

Faraday's law: the EMF induced in a circuit equals the NEGATIVE rate of change of magnetic flux through it.

For an N-turn coil: ε = −N·dΦ/dt. The minus sign is Lenz's law — encodes opposition.

Any way of changing flux generates EMF: moving the magnet, moving the coil, changing B, deforming the loop, rotating the loop.

Faraday discovered this experimentally (1831) by plunging a magnet through a coil and seeing the galvanometer kick.

EMF is proportional to the RATE of flux change — faster motion ⇒ bigger ε.

Direction of induced current is set by Lenz's law: induced B opposes the change in Φ.

Faraday's law is one of Maxwell's four equations and underlies generators, transformers, induction cooktops, microphones, electric guitars, and metal detectors.