Penetration of non-uniform electromagnetic field into conducting body




three-dimensional electromagnetic field, electromagnetic field formation, exact analytical solution, skin effect


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 impedance boundary condition for diffusion of non-uniform field into conducting half-space. 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 with respect to the vertical coordinate from the external magnetic field intensity at the interface.

Author Biography

Yu. M. Vasetsky, Institute of Electrodynamics of the National Academy of Sciences of Ukraine, Ukraine

Doctor of Technical Science, Professor


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How to Cite

Vasetsky, Y. M. . (2021). Penetration of non-uniform electromagnetic field into conducting body. Electrical Engineering & Electromechanics, (2), 43–53.



Theoretical Electrical Engineering