Electrodynamics. An introduction to experiment and theory. (Q2386502)

The monograph is essentially based on four-hour one semester freshman courses including three-hour courses with additional themes and exercises. It is a useful textbook for physics and electrical engineering students. The 470 pages long monograph comprises both experimental and theoretical parts of the subject and is based on a joint course of an experimental and a theoretical physicist. The well-written book is the fourth edition; the first was published in 1980. Especially, the fourth edition is extended by a chapter on relativistic electrodynamics in comparison to the third edition, published in 1997 [Zbl 0871.00013]. The book consists of 13 chapters divided into sections and partly subsections. The chapters are completed by 8 appendices concerning mathematics, 3 appendices containing SI units of the electromagnetism, physical constants, and electronic symbols, an index with the most important notions, and the solutions of problems formulated at the end of the chapters 2 until 13 and of two appendices. This section contains not only the solutions of the exercises but also the ways to get the answers. The text is completed by a number of figures and computer graphics for the representation of fields. Often a short description of the content and a list of the used quantities are put in front of the sections. A bibliography is not existent. The reader should have knowledge along with a good one-year course in calculus. Particularly, he should familiar with vector algebra, vector and tensor analysis, and some probability theory and statistics. But, he has the possibility if necessary to extend his mathematical working skills using the appendices of the book related to these topics. It should be mentioned that the appendices about vector algebra and analysis contain only the most important formulas of the corresponding subject. For more details the authors refer to their monograph [Mechanics. An introduction to experiment and theory. 4th revised ed. (German). Springer-Lehrbuch. Berlin: Springer (2005; Zbl 1064.70001)]. Other subjects of the mathematical appendices are the Maxwell-Boltzmann distribution, important notions of the theory of distributions including the Dirac delta distribution, space-averages of physical quantities, and the Fermi-Dirac function. In order to introduce the reader into electromagnetics Chapter 1 is devoted to experiments that are related to electrical charges and forces, conductors and dielectric media, and Coulomb's law. The Chapters 2 until 4 are devoted to electrostatics, i. e., the electrical fields do not depend on the time. The authors consider the electrostatics in the absence of matter, in the presence of conductors, and the electrostatics in dielectric media, respectively. Starting with Coulombs law the notions of the point charge, the electrical force, the superposition principle, the electrical field intensity, the electrical field, the charge density and the electric flux are introduced. Other topics of Chapter 2 are Gauss's law, the irrotationality of the electrostatic field, the field equations of the electrostatics, the graphical representation of the fields, the Poisson and the Laplace equation for the electrostatic fields, and the treatment of the electric dipol. Electrical fields influence conductors, the fields generate charge densities on the surfaces of the conductors. This phenomenon is demonstrated with some examples and experiments in Chapter 3. In conclusion the electrostatics in dielectric media are studied in Chapter 4. The terms permeability, electric susceptibility, and electric polarisation, and the corresponding field equations including a approximate microscopic deduction are presented. Other topics are the energy density of the electrostatic field and the refraction law for electrical fields. In the electrostatic case one has either no or only temporary (e. g. in the case of polarisation) displacements of the charge positions. The next three chapters are devoted to the charge transport in the vacuum and in matter. Chapter 5 starts with the definition of the density of the electrical charge (the current density) and of the electric current. The macroscopic and microscopic formulation of the current density is presented. The continuity equation for the current density is deduced. Other topics are conductivity, Ohm's law, Joule heating, circuits and Kirchhoff' laws, the ion transport in liquids, electrolysis, the conductivity in metals, and the ion and electron transport in the case of gas ionisation. Chapter 6 is devoted to the fundamentals of the charge transport in solids, that means, ideas of quantum theory and statistical mechanics are used to understand the existence and the properties of charge carriers. This view is important for the discussion of the properties of electronic components, such as transistors and diodes. The charge carriers in the solids, the electrons, represent an many-particle system of fermions. One considers this system at the absolute zero and at higher temperatures. The quantum states, the Pauli principle, the Fermi energy, the Fermi-Dirac function, and the Fermi-Dirac distribution are treated in order to describe the problems. Energy bands are considered in order to interpret the conduction properties of crystals. Conductors, isolators; semiconductors, dielectric media, metals, and doped semiconductors are characterized. While the last two chapters deal with the charge transport inside of conductors, Chapter 7 is concerned with the charge transport through interfaces: between metal and vacuum, metal and metal, and semiconductor and semiconductor. A number of experiments and technical details of diodes and transistors are described. The Poisson equation for semiconductors with \(pn\)-junction is deduced and solved. The next two chapters deals with magnetostatics. A moving charge produces a magnetic induction field and is influenced by other moving charges. Besides the definition of the corresponding quantities the Lorentz force including current generation and the Biot - Savart law are treated. The two basic differential equations of magnetostatics, the magnetic divergence equation and Ampére's law, are given, everything demonstrated by experiments. Chapter 9 is particularly devoted to magnetostatics in matter. Topics are e.g. dia- or paramagnetism in atoms, electrons and liquids, ferromagnetism; magnetic susceptibility, and hysteresis. Analogically to Chapter 5 a microscopic formulation of the magnetostatic field equations is presented. In Chapter 10 the field equations in the stationary case ( the field equation of electrostatics and magnetostatics) are summarized and extended to the time-dependent quasi-stationary case, that means the fields are only slowly changeable. The rotation of the electrical field is now additionally related to the time derivative of the magnetic field (first Maxwell equation). This simplification in relation to the fully time-dependent Maxwell's equations can be used if the (physical size of the system) \(\times\) (frequency) \(\ll\) (velocity of light). Amongst others self- and mutual inductances, magnetic energy, and eddy currents are treated. Chapter 11 contains a general discussion of Maxwell's equation. Additionally, Ampére's law (second Maxwell equation) is now extended by the derivative of the electric field. The differential and the integral form of Maxwell's equations are discussed. Potentials of the electromagnetic field, gauge transformations, the d'Alembert equation, the Lorentz and the Coulomb gauge, conservation laws, and the poynting vector are introduced. The Maxwell stress tensor is derived. Analogically to Chapter 5 and 9, a microscopic motivation of the time-depended field equations in matter is presented. Electromagnetic waves as solutions of Maxwell's equations are the subject of Chapter 12. Discussed are amongst others plane waves, standing waves, dipols, antennas, superposition of waves, interference; polarisation, a solution of the inhomogeneous d'Alembert equation using the Green function, and Liénard-Wiechert potentials. The last chapter is devoted to special relativity in electrodynamics. The authors starts with basic concepts, such as Einstein's postulates, Lorentz transformation, time dilatation, space contraction, Minkowski geometry, vectors in four dimensions, and go over to the relativistic equation of motion, the Minkowski force, and the Lorentz transformation of the electromagnetic fields getting the electromagnetic field equations in the relativistic formulation with the most important details adequate to the treated classic theory.