Penetration of Non-uniform Sinusoidal Electromagnetic Field into Conducting Half-Space

The study is based on the exact analytical solution for the general conjugation problem of three-dimensional quasi-stationary field at a flat interface between dielectric and conducting media. It is determined that non-uniform electromagnetic field always decreases in depth faster than uniform field. The theoretical conclusion is confirmed by comparing the results of analytical and numerical calculations. The concept of strong skin effect is extended to the case when penetration depth is small not only compare to the characteristic body size, but also when the ratio of the penetration depth to the distance from the surface of body to the sources of the external field is small parameter. For strong skin effect in its extended interpretation, the influence of external field non-uniformity to electromagnetic field formation both at the interface between dielectric and conducting media and to the law of decrease field in conducting half-space is analyzed. It is shown, at the interface the expressions for the electric and magnetic intensities in the form of asymptotic series in addition to local field values of external sources contain their derivatives with respect to the coordinate perpendicular to the interface. The found expressions made it possible to generalize the approximate Leontovich’s impedance boundary condition for diffusion of non-uniform field into conducting half-space. The function that generalizes the impedance boundary condition in the case of diffusion of non-uniform field into conducting body is proposed. Based on comparison of the calculations results by the exact and approximate methods for a specific model of an electromagnetic system, the permissible maximum value of the introduced small parameter is established. The difference between the penetration law for the non-uniform field and the uniform one takes place in the terms of the asymptotic series proportional to the small parameter to the second power and to the second derivative from the external magnetic field intensity at the interface with respect to the vertical coordinate.