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In the latest issue of The Physics Teacher, Brahmia and Horton raise the
question of whether the "induction cooktop" really utilizes the induction
of current to warm up the pan. They note that a ferromagnetic pan is
needed and this implies an hysteresis effect.
Back as a postdoc (ten years ago already!) I worked with induction heating.
I don't remember the exact equations right now, but the size of the induced
current depends on the size & frequency of the external field, on the size
and geometry of the sample, and on the resistivity and permeability of the
sample. Basically, as you go from a realtive permeability of 1 for a
"normal" metal to perhaps several thousand for a soft magnet, the heating
also goes up by several thousand (or maybe square root of a several
thousand, but you get the point). Thus it is easy to inductively heat a
chunk of iron to just below the curie temperature, but much more difficult
to go higher.