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Wikipedia[1] claims:

An induction cooker uses a type of induction heating for cooking. It is chiefly distinguished from other common forms of stovetop cooking by the fact that the heat is generated directly in the cooking vessel, as opposed to being generated in the stovetop by electrical coils or burning gas. To be used on an induction cooker, a cooking vessel must be made of a ferromagnetic material and be electrically conductive.
In an induction stovetop, a coil of copper wire is placed underneath the cooking pot. An alternating current|alternating electric current is made to flow through the coil, which produces an oscillating magnetic field which creates heat in the cooking vessel over it in two different ways. Principally, it induces an electric current in the pot, which produces resistive heating proportional to the square of the current and to the electrical resistance of the vessel. Secondly, it also creates magnetic hysteresis losses in the pot due to its ferromagnetic nature. The first effect dominates: hysteresis losses typically account for less than ten percent of the total heat generated.[2]

Induction cookers are faster and more energy-efficient than traditional electric cooktops; moreover, they allow instant control of cooking energy, which no energy source other than gas offers. Because induction heats the cooking vessel itself, the possibility of burn injury is significantly less than with other methods: only skin contact with the cooking vessel itself (or, when high heat has been used, the stovetop for a while after the vessel has been removed) can cause harm. There are not the high temperatures of flames or red-hot electric heating elements found in traditional cooking equipment, which generates heat independent of the cooking vessel. Further, induction cookers do not themselves warm the surrounding air, resulting in further energy efficiencies.

It is possible to build an induction cooker that works with any pot that conducts electricity (a pot made of any metal, but not of an electrically insulating material such as glass or ceramic), even if the pot is not ferromagnetic, but the increased permeability of an iron or steel pot makes the system substantially more practical by increasing the inductance seen by the drive coil and by decreasing the skin depth of the current in the pot, which increases the AC resistance for the I2R heating.[3] Most practical induction cookers are designed for ferromagnetic pots; users are advised that the cooker will work only with pots to which a magnet will stick.

Since heat is being generated by an induced electric current, the unit can detect whether cookware is present (or whether its contents have boiled dry) by monitoring the voltage drop caused by resistance in the circuit (which reflects how much energy is being absorbed). That allows such functions as keeping a pot at minimal boil or automatically turning an element off when cookware is removed from it.