Electromagnetic Field of Arbitrary Spatial Current Contour Located Near Conducting Body with Flat Surface

In the chapter, the studies are aimed at the exact analytical solution of a three-dimensional quasi-stationary problem, which is formulated in a fairly general setting. It is necessary to find the electromagnetic field of an arbitrary spatial contour with an alternating current, located above a conductive magnetizable half-space, in which eddy currents are induced. Restrictions are not imposed on the geometry of the contour with current and its orientation relative to the interface of dielectric and conducting media, the electrophysical properties of media and the field frequency. A linear task is considered, which, based on the principle of superposition, can easily be extended to the general case of an arbitrary system of the contours, that is, an arbitrary location of external field sources, as well as an arbitrary dependence of the current on time using the Fourier transform in time. The analytical solutions for the vector and scalar potentials, electric and magnetic field intensities are defined both in dielectric and conducting media. The main feature of quasi-stationary electromagnetic field formation for system with plane interface between the dielectric and conducting media is determined—the components of electric intensity and current density which are perpendicular to boundary surface are not available (equal to zero) in the conducting medium. This property holds true for any spatial configuration of the initial system of current and for any time dependence of external field sources. The physical reason for the absence of vertical components of the current density and electric field intensity in the conducting half-space is the appearance of a distributed electric charge on the interface surface, the field of which in the conducting half-space completely compensates for the vertical component of the external induced electric field. At the surface in the dielectric area the vertical component of the electric field intensity is twice the vertical component of the known induced field of the sources.