The vector potential has been obtained for a coil coaxial with an arbitrary number of cylindrical conductors. The derivation is quite general and employs an iterative process that has been adapted to computer programs. After the vector potential has been obtained, it is used to calculate the mutual and self‐impedance of multiple and single coils, the effect of defects in the conductors on the mutual and self‐impedances, and the induction heating density in the conductors.