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Overview
The book may be divided into three parts: field analysis, basic electromagnetic theory, and applications. Basic laws and concepts — along with their implications — are thoroughly discussed before detailed mathematical analysis is undertaken. In addition to rigorous treatments of all relevant derivations and proofs, appropriate emphasis is placed upon the physical significance of mathematical operations.
Product Details
| ISBN-13: | 9780486832821 |
|---|---|
| Publisher: | Dover Publications |
| Publication date: | 05/15/2019 |
| Series: | Dover Books on Physics |
| Pages: | 544 |
| Product dimensions: | 5.90(w) x 8.90(h) x 1.20(d) |
About the Author
Read an Excerpt
PREFACE
This text contains sufficient material for a three-term, three-hour-per-week course. It is, however, primarily intended for a two-term undergraduate course in which the individual instructor may choose from among a variety of optional topics for detailed treatment. If the student has had prior training in advanced calculus (or if the text is used for graduate studies), it may be possible to treat the first four chapters as review material, with emphasis placed on the physical interpretation of mathematical relations. Such a review will also serve the purpose of familiarizing the reader with the notation introduced in these chapters and used throughout the text.
Depending on the requirement of _the undergraduate curriculum, many sections and some of the proofs may be omitted to provide shorter courses. These sections and proofs are marked, and their omission does not break the continuity of the text. In most cases we have first stated what is to be proved before proceeding to prove it. This makes it possible to use the text with varying degrees of mathematical involvement. The authors have found that the availability of detailed derivation in the text makes it possible to use the classroom hours for a discussion of the physical significance of the results and for problem solving, rather than for a reproduction of the derivations.
The problems given at the end of the text are designed to complement and extend the text material. For this reason they are numbered by chapter, section, and problem. For example, Prob. 1-4.3 deals with material discussed in Sec. 1-4 and is the third such problem. This numbering will assist the reader in locating the pertinent discussion. Throughout the text the rationalized mks-coulomb system of units is used and, for brevity, units of various quantities are not always explicitly stated.
The principal motivation for writing this text is best understood in terms of our objections to some of the currently available treatments of the subject. Although many undergraduate texts in electromagnetics have been published during the past decade, most of these are written with the idea that field theory is really graduate material and that there is no need to deal with it in depth at the undergraduate level. The courses based on such texts include only that mathematical preparation which is essential to solve the problems at hand ; they do not provide the student with reasonable preparation for graduate studies. In accordance with this philosophy, the laws of electromagnetic theory are introduced piecemeal, so that the student does not learn a law in any greater generality than is necessary to solve the next set of problems.
Because of the lack of depth in such courses, most graduate schools have to start their field analysis and electromagnetic theory from "scratch," ignoring the undergraduate training of students. In fact, it is not an unusual experience to find such a training a hindrance rather than a help to graduate studies, inasmuch as some of the oversimplified concepts learned in undergraduate studies must be unlearned before more exact concepts can replace them. Furthermore, the low level of analysis currently prevalent in undergraduate courses in electromagnetic theory is inconsistent with the fact that in many schools advanced calculus is now taught to engineering students.
Notwithstanding this background in advanced calculus, it has been our experience that the formal approach of mathematics courses does not adequately prepare the student for the application of this material to physical problems. For this reason we have found it necessary to devote the first five chapters of the text to field analysis, in which we introduce the concepts of divergence, curl, and laplacian, not as mere differential operators, but as volume densities of the sources of a field. Similarly, a uniqueness theorem is treated not only as a mathematical structure but also as an expression of what constitutes physical determinism. We have found this approach most effective with students whether or not they have taken a course in advanced calculus.
In addition to the preparation for the study of electromagnetics, the first five chapters provide a self-contained and sound basis for the mathematical analysis of all kinds of fields and should prove valuable to physicists and mechanical, chemical, and civil engineers as well as electrical engineers.
With the introduction of the general concepts of fields and their sources, it is possible to state the laws of electromagnetic theory in an integrated manner. This is done in Chapter 6 where, in addition to Maxwell's equations, the concepts of energy conservation (Poynting's theorem) and electromagnetic momentum, as well as electromagnetic waves and potentials, are introduced. This chapter is a complete statement of the classical laws of electromagnetic theory, and the rest of the text is concerned with developing the ramifications of the theory and with its application to practical problems. Chapter 7 is devoted to introducing the technique of multi pole expansion and the use of electric and magnetic multipole approximations. Chapter 8 deals, in detail, with the consequences of idealizations made in practice, where distributed charges and currents are assumed to be singular in the form of surface or line densities or point sources. This and the assumption of abrupt boundaries between two media lead to (nonphysical) discontinuities in the electric and magnetic fields at the idealized boundaries. The chapter shows how these idealizations are used to solve practical problems. The use of the Green's function and the concepts of coefficients of inductance and capacitance are also introduced in this chapter. Chapter 9 contains a detailed discussion of the method of separation of variables as applied to the solution of boundary-value problems. Also included in this chapter are numerical and graphical methods for solving problems whose boundaries do not permit direct analysis. Some microscopic properties of matter are considered in Chapter 10. In Chapter 11, radiating fields are introduced by means of a discussion of the elementary dipole antenna. Radiating fields are then contrasted with quasi-static fields-leading to a discussion of the field basis of circuit theory. Chapter 12 contains a comprehensive analysis of plane waves and applies this analysis to the study of transmission lines and waveguides. The general relationships between the transverse and longitudinal components of a plane wave derived in this chapter provide the basis for the study of guides of arbitrary cross section, although only rectangular guides are treated in detail.
Chapter 13 is an introduction to propagation in lossy media; it ends with a discussion of dispersion due to lossiness of the medium as well as geometric and parametric dispersion. Chapter 14 deals with the reflection of plane waves and the exchange of momentum between an electromagnetic field and a material medium. Chapter 15 uses the formulas derived in Chapter 11 as a basis for analyzing radiation from linear and loop antennas. This final chapter concludes with a discussion of antenna arrays and receiving antennas.
The material of this text has been taught by the authors and some of their colleagues from notes for the last three years at The City College of New York.
The authors wish to thank Professor John Truxal, Vice President in charge of Education at the Polytechnic Institute of Brooklyn, for his encouragement and help throughout the preparation of the manuscript. Thanks are also due to our Department Chairman, Professor Herbert Taub, for his cooperation. The authors have benefited from long discussions with many of our colleagues-most particularly, with Professor Egon Brenner of The City College and Professor Leonard Bergstein of the Polytechnic Institute of Brooklyn. Words cannot express the depth of our gratitude to Miss Sadie Silverstein, without whose cooperation in preparing the manuscript this text could not have been published. We are also grateful to our former student, Miss Rosalind Soodak, for drawing most of the original figures. Finally, we wish to thank our students who have suffered through early drafts and have provided us with innumerable corrections.
Mansour Javid Philip Marshall Brown
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