Vol. 92

Latest Volume
All Volumes
All Issues

Nonuniform Electromagnetic Field at the Interface Between Dielectric and Conducting Media

By Yuriy Vasetsky
Progress In Electromagnetics Research Letters, Vol. 92, 101-107, 2020


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.


Yuriy Vasetsky, "Nonuniform Electromagnetic Field at the Interface Between Dielectric and Conducting Media," Progress In Electromagnetics Research Letters, Vol. 92, 101-107, 2020.


    1. Babutsky, A., A. Chrysanthou, and J. Ioannou, "Influence of pulsed electric current treatment on corrosion of metals," Strength of Materials, Vol. 41, No. 4, 387-391, 2009.

    2. Batygin, Yu. V., S. F. Golovashchenko, and A. V. Gnatov, "Pulsed electromagnetic attraction of nonmagnetic sheet," Journal of Materials Processing Technology, Vol. 214, No. 2, 390-401, 2014.

    3. Acero, J., R. Alonso, J. M. Burdio, L. A. Barragan, and D. Puyal, "Analytical equivalent impedance for a planar induction heating system," IEEE Transaction on Magnetics, Vol. 42, No. 1, 84-86, 2006.

    4. Rudnev, V., D. Loveless, R. Cook, and M. Black, Handbook of Induction Heating, Taylor & Francis Ltd, London, 2017.

    5. Leontovich, M. A., "On the approximate boundary conditions for electromagnetic field on the surface of highly conducting bodies," Propagation of Electromagnetic Waves, USSR Academy of Sciences Publ., Moscow-Leningrad, USSR, 1948 (in Russian).

    6. Fridman, B. E., "Skin effect in massive conductors used in pulsed electrical devices: I. Electromagnetic field of massive conductors," Technical Physics, Vol. 47, No. 9, 1112-1119, September 2002.

    7. Cacciola, M., F. C. Morabito, D. Polimeni, and M. Versaci, "Fuzzy characterization of flawed metallic plates with Eddy current tests," Progress In Electromagnetics Research, Vol. 72, 241-252, 2007.

    8. Versaci, M., "Fuzzy approach and Eddy currents NDT/NDE devices in industrial applications," IET Electronics Letters, Vol. 52, No. 11, 943-945, 2016.

    9. Rytov, S. M., "Calculation of skin effect by perturbation method," Journal of Experimental and Theoretical Physics, Vol. 10, No. 2, 180-190, 1940 (in Russian).

    10. Kravchenko, A. N., Boundary Characteristics in Electrodynamics Problems, Naukova Dumka, Kyiv, 1989 (in Russian).

    11. Berdnik, S. L., D. Y. Penkin, V. A. Katrich, Yu. M. Penkin, and M. V. Nesterenko, "Using the concept of surface impedance in problems of electrodynamics (75 years later)," Radio Physics and Radio Astronomy, Vol. 19, No. 1, 57-80, 2014.

    12. Vasetskyi, Yu. M. and K. K. Dziuba, "An analytical calculation method of quasi-stationary three-dimensional electromagnetic field created by the arbitrary current contour that located near conducting body," Technical Electrodynamics, No. 5, 7-17, 2017 (in Russian).

    13. Vasetsky, Yu. M. and K. K. Dziuba, "Three-dimensional quasi-stationary electromagnetic field generated by arbitrary current contour near conducting body," Technical Electrodynamics, Vol. 1, 3-12, 2018.

    14. Vasetsky, Yu., I. Mazurenko, and K. Dziuba, "Conditions for application of asymptotic method to electromagnetic field analysis in system of “a current loop — An electroconducting body”," Computational Problems of Electrical Engineering, Vol. 4, No. 1, 91-96, 2014.