Although the description of the working mechanism of an induction cooktop is often popularly described as based on eddy currents, this by itself does not clearly point out the operating principles of their use.
1. Eddy currents result from a changing magnetic field in a conducting material with bulk resistance. For a given external magnetic field, a ferrous metal cooking vessel will have higher internal magnetic field, hence stronger eddy currents. The changing magnetic field tries to produce a compensating magnetic field caused by the eddy currents. This mechanism acts as a current source in the material, not a voltage source, for low resistances.
2. The heating due to the eddy currents will increase as the effective resistance of the pot surface increases. One way to do this is to concentrate the current in a thinner layer of the ferrous metal. One way to do this and still have a sturdy pot bottom is to make use of skin effect. To get a useful skin effect contribution, frequencies higher than 60Hz need to be used. 10kHz or higher frequency gives reasonable results.
3. Since the induction coil operates at other than line frequency, a DC power supply driving an oscillator is needed. Once you introduce a DC supply, it is relatively cheap and also useful to design it to produce a constant output voltage from a range of input voltages. Use of this design makes it possible to deliver the same heat output from 208 volt input as from 240 volt input, as long as the input current is allowed to rise.