Electromagnetic induction

A changing magnetic field passing through a loop of wire induces an electromotive force in that loop — Faraday's discovery that electricity and magnetism are two sides of the same coin. Crucially, it's a changing field that matters; a steady, unchanging field through a stationary loop induces nothing at all.

There's more than one way to make the field "change" from the loop's point of view. You can vary the field's strength while the loop sits still, move the loop into or out of a steady field, or rotate the loop within a steady field so the amount of field passing through it keeps changing — all of these count as a changing magnetic flux, and all of them induce an EMF.

The faster the flux changes, the larger the induced EMF, not the stronger the field alone. Yanking a magnet quickly through a coil produces a bigger voltage spike than sliding the same magnet through slowly, even though the magnet's strength never changed — this is the whole operating principle behind generators, which spin coils through magnetic fields to produce a continuous supply of electricity.