The alternator: producing electricity

Induction is not a laboratory curiosity: it produces nearly all the electricity you use. The key device is the alternator. Its principle: spin a coil in a magnetic field (or a magnet in front of a coil). As it turns, the angle θ constantly changes, so the flux constantly varies, so an e.m.f. is continuously induced.

   coil spinning in a field B
        _____
       /  |  \        θ changes continuously -> Φ = B·A·cos(θ) varies
      | (((|))) |  <- rotation
       \__|__/
                     -> alternating induced e.m.f. (reverses each half-turn)

Since the flux rises then falls each half-turn, the induced voltage changes sign periodically: it is an alternating current (mains current, at 50 Hz in Europe). Where does the energy come from? From whatever spins the coil.

   dam (water)        ->  turbine  ->  alternator  ->  electricity
   steam (nuclear, gas) -> turbine ->  alternator  ->  electricity
   wind               ->  blades   ->  alternator  ->  electricity

Hydro, nuclear, thermal, wind plants: all do the same thing deep down — spin an alternator. Only the driving source differs. The solar panel is the great exception (it uses the photoelectric effect, not induction).

So an 1831 experiment with a magnet and a coil became the heart of all the world's electricity production. To understand induction is to understand where the current from the socket comes from.