Analytical determination of a quasi-stationary electromagnetic field created by magnetic moments and eddy currents in conducting half-space

Abstract

Aim. Study of the distribution of a three-dimensional alternating quasi-stationary electromagnetic field at the surface of conducting half-space with strong skin-effect, the source of which is an arbitrarily oriented magnetic moment. Methodology. The expressions for non-uniform electromagnetic field with strong skin effect are used for the analysis, which is based on the found exact analytical solution of the general three-dimensional problem and the use of expansion into asymptotic series with respect to a small parameter that is proportional to the ratio of the field penetration depth to the distance between the sources of the external field and the surface of body. Specific expressions at the surface are completely determined by the known field of external sources. In this work, the external magnetic moment field is used. Results. For strong skin effect, expressions for the electric and magnetic field strength are obtained separately for the components of the magnetic moment oriented perpendicularly and parallel to the flat surface between the dielectric and conducting areas. The features of the electromagnetic field distribution are analyzed depending on the value of introduced small parameter. The results are presented for the module and phase shift of the field strength with respect to the phase of the external field source. Originality. The expressions found for the electromagnetic field appear to be more general than the use of closed contours with alternating current, since they extend types of external field sources and allow the use of the superposition method instead of integration over the entire contour. Practical value. The found specific analytical expressions of the electromagnetic field at the surface for the external field of magnetic moments significantly simplify the solution of the problems, since they do not require additional solution of the field equations. References 20, figures 8.