Electromagnetic Field Near Conducting Half Space

The book is devoted to the solution of one general problem of the theory of a three-dimensional quasi-stationary sinusoidal and pulse electromagnetic field. These studies, unlike many well-known works, are based on obtained exact analytical solution of the problem for the field, generated by external current sources near the conducting body with plane surface. The solution for the vector and scalar potentials, electric and magnetic intensities in the dielectric and conducting media is found without restrictions on the configuration of current sources, properties of the media and field frequency. Some general properties of field formation for arbitrary field in the considered system are obtained (in particular, full compensation by the field of the electric charge distributed on the interface between the media, the normal component of the induced external electric field and, accordingly, the equality to zero the components both of the current density and the electric field intensity perpendicular to the interface; the non-uniform electromagnetic field decreases in depth of conducting medium faster than uniform field). It is shown that the exact analytical solution depends on the values of the parameter proportional to the ratio of the field penetration depth to the distance between the external field sources and the body. The concept of strong skin effect is extended to the case of small value of the introduced parameter. A significant simplification of the expressions was obtained as an asymptotic expansion on this small parameter. In the case of pulsed fields approximate method gives the highest accuracy during important initial period of pulse time. For asymptotic expansion the approximate impedance boundary condition is generalized to the diffusion of non-uniform field into conducting medium. The book is intended for the researchers, postgraduate students and students specialized in theory and calculations of electromagnetic fields.

The book combines two interrelated lines of research. One of them is devoted to the development of the theory for solving a certain class of three-dimensional electromagnetic field problems of the three-dimensional electromagnetic field, taking into account eddy currents in a moving conducting magnetizing body. Preference is given to the development of the analytical solution methods of the three-dimensional quasi-stationary problem of field conjugation in the system: “a contour of an arbitrary spatial configuration with an alternating current is conducting body with a flat boundary surface”. The second direction refers to the development of mathematical models for solving applied problems, which involve the use of developed methods for calculating the electromagnetic field and their characteristics. The main application of calculation methods is aimed at solving problems of heat treatment non-ferrous and ferrous metal products using the induction method of heating in a transverse magnetic field. The inverse problems are solved to determine the inductor configuration as flat and spatial current contours for providing the necessary temperature distribution of moving metal strips. To achieve uniform heating of strips across the width using inductors in the form of flat current contours parallel to the strip surface, it is advisable to use combinations of current contours, where the geometric dimensions are determined by the size and electro-physical parameters of the metal strips. A more uniform temperature distribution during high-frequency induction heating is achieved by using inductors in the form of current contours of the required spatial configuration. The book is intended for researchers, postgraduate students, and students specialized in theory and calculations of electromagnetic fields and induction heating installations.

This is a textbook designed to provide analytical background material in the area of Engineering Electromagnetic Fields for the senior level undergraduate and preparatory level graduate electrical engineering students. It is also an excellent reference book for researchers in the field of computational electromagnetic fields. The textbook covers ? Static Electric and Magnetic Fields: The basic laws governing the Electrostatics, Magnetostatics with engineering examples are presented which are enough to understand the fields and the electric current and charge sources. Dynamic Electromagnetic Fields: The Maxwell's equations in Time-Domain and solutions, the Maxwell's equations in Frequency-Domain and solutions. Extensive approaches are presented to solve partial differential equations satisfying electromagnetic boundary value problems. Foundation to electromagnetic field radiation, guided wave propagation is discussed to expose at the undergraduate level application of the Maxwell's equations to practical engineering problems.

"Electromagnetic Fields in Stratified Media" deals with an important branch of electromagnetic theory, which has many useful applications in subsurface communication, radar, and geophysical prospecting and diagnostics. The book introduces to the electromagnetic theory and wave propagation in complex media, while presenting detailed models for various media: 3, 4, N-layered media, boundary conditions, and anisotropic media. In particular, the complete solutions for a trapped surface wave and lateral wave in a three- or four-layered region, the complete solutions for low frequency wave propagation over a spherical surface coated with a dielectric layer, and the transient field of a horizontal dipole in the boundary layer of two different media are presented. The book is designed for the scientists and engineers engaged in antennas and propagation, EM theory and applications. Dr. Kai Li is Professor at Zhejiang University.