Impedance of a horizontal coil above a conducting half-space

The induction of eddy currents by a circular, air-cooled coil of rectangular cross section, carrying a low-frequency alternating current and with its axis parallel to the surface of a homogeneous conducting half-space is considered. An exact, closed-form expression for the coil impedance is derived. The calculations are in excellent agreement with experiment and agree with an independent calculation of coil impedance which is valid in the limit of small skin depth.