Three-Dimensional Quasi-Stationary Electromagnetic Field Generated by Arbitrary Current Contour Near Conducting Body

Abstract

The analytical method is developed to calculate the three-dimensional quasi-stationary electromagnetic field generated by arbitrary spatial current contour near the conducting body 1 / 3 2018 N1 st1 with plane surface. By the use of displacement currents in dielectric region under quasi-stationary approximation, in addition to the results presented earlier, the solution for the scalar potential and electric intensity in entire dielectric half-space is found. Owing to the established fact of vertical zero components of the electric intensity and current density in conducting half-space, the electric field of surface charge compensates completely the vertical component of induced electric intensity of the initial current system. As an example, the electric intensity and surface electric charge density are calculated for the current contour configuration typical for technological systems. References 13, figures 3.

Nonuniform Electromagnetic Field at the Interface Between Dielectric and Conducting Media

“…An analytical solution to the linear problem of determining the electromagnetic field generated in a system containing an arbitrary current contour and a conducting body with a flat surface modeled by a conducting half-space was obtained in [12,13]. The solution was obtained without restrictions on the geometry and orientation of the contour, the electrophysical properties of the medium (electrical conductivity γ i and relative magnetic permeability μ i ), and the frequency of the field ω.…”

“…A feature of this study is that it is based on the exact analytical solution obtained for the general problem of a three-dimensional quasi-stationary field [12,13]. In particular, the main property of the formation of electromagnetic field with a flat interface has been established.…”

Exact Analytical and Approximate Asymptotic Calculation Methods to Determine Three-Dimensional Electromagnetic Field Near Conducting Body With Flat Surface

“…Therefore, simplification of calculations is an important task. For this purpose, an approximate asymptotic method can be used, which is valid in the case of a strong skin effect [19,22].…”

“…Expressions ( 15) and ( 16) for the intensities of the electromagnetic field at 0  z are greatly simplified. Here at strong skin effect the electromagnetic field is determined only by the known distribution of the field of external sources at the boundary without the need to solve additional equations [20,22]:…”

“…for specific points 1 M not related to the configuration of the contour was studied in sufficient detail in [22]. Therefore, here we will compare the calculation of threedimensional electromagnetic field for a model of an electromagnetic system with circular contour with sinusoidal current [3] (Fig.…”