Approximate Mathematical Models for Analysis of Alternating Electromagnetic Field of Sources Near Conducting Body

Approximate mathematical models for calculating three-dimensional electromagnetic fields are developed and analyzed on the basis of the exact analytical solution found for the problem of determining the three-dimensional quasi-stationary field of arbitrary external sources near conducting half-space. From the standpoint of the general electromagnetic field, the simplest model of the perfect skin effect is considered. It is shown that the normal component of the electric field intensity and the surface density charge on the surface are completely determined by the normal component of the induced electric field of external sources. For the case of small but finite field penetration depth the method of expand exact analytical expressions into asymptotic series has been developed to based on the introduction of a small parameter that generalize the concept of strong skin effect. The strong skin effect is understood as its extended definition, when not only the penetration depth of the alternating field is small compared to the characteristic dimensions of the conducting body, but the ratio of the penetration depth to the characteristic dimensions of the entire electromagnetic system is also small, including the distances between external field sources and conducting body. Unlike the original expressions, which contain improper integrals from special functions, the specific expressions found are bounded asymptotic series, where each term is found by calculating only one-dimensional contour integral. It is established that the required accuracy is achieved by using the first few terms of the series, the number of which depends on the value of the introduced small parameter. It is substantiated that the possibility of further simplification of calculations using the model of a locally two-dimensional field, which allows the replacement of contour integrals by simple algebraic expressions. The mathematical model is valid when determining the electromagnetic field in the area near initial conductor with current near interface of media. Calculations are limited to systems with a small angle of inclination of the contour sections to the interface, which is due to the neglect of the electromagnetic field component associated with the current component normal to the flat surface.