How Induction Cooking Works:
The element's electronics power a coil (the red lines) that produces a high-frequency electromagnetic field (represented by the orange lines).
That field penetrates the metal of the ferrous (magnetic-material) cooking vessel and sets up a circulating electric current, which generates heat. (But see the note below.)
The heat generated in the cooking vessel is transferred to the vessel's contents.
Nothing outside the vessel is affected by the field--as soon as the vessel is removed from the element, or the element turned off, heat generation stops.