At the Palais de la Decouverte in Paris, they showed me this experiment where a 1kg aluminium plate is levitated above a large coil of wire that is being supplied with 800A of alternating current at 900Hz. This is by far the best demonstration of electromagnetic induction I have ever seen.
Back in London, I visited the magnetic lab of Michael Faraday in the basement of the Royal Institution. It was here that he did his groundbreaking work on induction. People had previously observed that current in a wire causes a compass needle to deflect, but more exciting was the prospect of using a magnetic field to generate current. Faraday created his famous induction ring by winding two coils of insulated wire onto an iron ring. When he connected a battery to one coil, a small pulse of current was induced in the other. When the battery was disconnected, current was induced in the other direction. This led Faraday to the conclusion that current was induced in the second coil only when the magnetic field through it was changing.
And if they hadn't been wrapped on the same ring, Faraday may have noticed that the two coils repel each other when the current is induced due to the interaction of their magnetic fields. This is the same thing that is happening with the aluminium plate, except we're using alternating current to create a continually changing magnetic field. This induces an alternating current in the plate, producing an opposing magnetic field which levitates the disk.