A general derivation is performed to determine the vector potential produced by eddy current coils concentric with multiple cylindrical conductors. The conductors may be inside the coils, encircling the coils, or both. From the vector potential certain physical phenomena, such as coil impedance, mutual coupling between coils, effect of defects, and ohmic heating, are calculated. The coils may be placed in electrical circuits and the voltages produced are calculated.
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