Faraday's law of induction

Faraday's law is the discovery that a changing magnetic field conjures an electric voltage out of thin air — magnetism leaking into electricity. Wave a magnet toward a loop of wire and a current springs up in the loop; yank it away and the current reverses. The wire doesn't care about the magnet's strength, only about how fast the magnetic flux threading the loop is changing. Hold the magnet still and nothing happens, no matter how strong it is; it's the motion, the change, that does the work.

Spelled out, the induced voltage equals the rate of change of magnetic flux through the loop (with a minus sign that captures Lenz's law: the induced current always opposes the change that made it). This single idea powers civilization. Every generator in every power plant spins a coil through a magnetic field to make the 50 or 60 Hz on your wall; every transformer relies on a flux that rises and falls 100 times a second to step voltage up or down; and the wireless charging pad under your phone is Faraday's law working across a millimetre of air.