Abstract
A simple scalar representation is used to describe the electromagnetic field in the quasi-static limit for an arbitrary time-harmonic source current above an imperfectly conducting half-space. Solutions are given in terms of half-space scalar and dyadic Green’s functions. The general results are then used to derive analytical expressions for the fields arising from circular filaments and extended sources whose axes of symmetry are parallel to the surface of the conductor. These tangent coil solutions have applications in the theory of inductive sensors, particularly for eddy current nondestructive testing.

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