The study of the electromagnetic field, taking into account eddy currents in the conductive half-space, is based on the exact analytical solution of the general three-dimensional quasi-stationary problem. The mathematical model includes an approximate solution using asymptotic expansion in the case of strong skin effect. Analytical expressions are obtained for the electric and magnetic fields at a flat interface in the form of limited asymptotic series, each term of which is expressed through a known field of external sources. The expressions take into account the nonuniformity of the field near the surface, since they contain its derivatives with respect to the coordinate. The series expansion was carried out according to a small parameter, which is proportional to the ratio of the field penetration depth to the distance between the interface and the sources of the external field. The found expressions generalize the approximate boundary impedance condition for the case of the penetration of nonuniform electromagnetic field into conductive medium.
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