Impedance of a cylindrical coil over an infinite metallic half-space with shallow surface features

An analytical solution is derived for the electric and magnetic fields produced by an air-core cylindrical coil driven by a constant ac current source and placed over an infinite metallic half-space with small surface perturbations. The depth of the features on the half-space is small compared to the mean radius of the coil. The perturbation technique is used to solve the Maxwell equations in the quasistatic approximation. Formulas are given for the electric field and the impedance. Real and imaginary parts of the impedance are computed and plotted for several test cases.