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'Eddy currents' are a circulating currents set up as a result of voltages induced into a metal component which not intended to carry current. For example, eddy currents are induced into the silicon-steel core of a transformer due to voltages induced into the core by the changing currents in the transformer's windings. Eddy currents are unavoidable, although steps can be taken to minimise them -in the case of a transformer's core, by manufacturing the core from laminations. Eddy currents generally have no useful function, but represent energy losses. To answer your question directly, eddy currents can only exist in conducting materials.

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