This book is designed for use as an undergraduate text on engineering electromagnetics. Electromagnetics is one of the most fundamental subjects in an electrical engineering curriculum. Knowledge of the laws governing electric and magnetic fields is essential to the understanding of the principle of operation of electric and magnetic instruments and machines, and mastery of the basic theory of electromagnetic waves is indispensable to explaining action-at-a-distance electromagnetic phenomena and systems.
Because most electromagnetic variables are functions of three-dimensional space coordinates as well as of time, the subject matter is inherently more involved than electric circuit theory, and an adequate coverage normally requires a sequence of two semester-courses, or three courses in a quarter system. However, some electrical engineering curricula do not schedule that much time for electromagnetics. The purpose of this book is to meet the demand for a textbook that not only presents the fundamentals of electromagnetism in a concise and logical manner, but also includes important engineering application topics such as electric motors, transmission lines, waveguides, antennas, antenna arrays, and radar systems.
I feel that one of the basic difficulties that students have in learning electromagenetics is their failure to grasp the concept of an electromagnetic model. The traditional inductive approach of starting with experimental laws and gradually synthesizing them into Maxwell's equations tends to be fragmented and incohesive; and the introduction of gradient, divergence e, and curl operations appears to be ad hoc and arbitrary. On the other hand, the extreme of starting with the entire set of Maxwell's equations, which are of considerable complexity, as fundamental postulates is likely to cause consternation and resistance in students at the outset. The question of the necessity and sufficiency of these general equations is not addressed, and the concept of the electromagnetic model is left vague.
This book builds the electromagnetic model using an axiomatic approach in steps--first for static electric fields, then for static magnetic fields, and finally for time-varying fields leading to Maxwell's equations. The mathematical basis for each step is Helmholtz's theorem, which states that a vector field is determined to within an additive constant if both its divergence and its curl are specified everywhere. A physical justification of this theorem may be based on the fact that the divergence of a vector field is a measure of the strength of its flow source and the curl of the field is a measure of strength of its vortex source. When the strengths of both the flow source and the vortex source are specified, the vector field is determined.
For the development of the electrostatic model in free space, it is only necessary to define a single vector (namely, the electric field intensity E) by specifying its divergence and its curl as postulates. All other relations in electrostatics for free space, including Coulomb's law and Gauss's law, can be derived from the two rather simple postulates. Relations in material media can be developed through the concept of equivalent charge distributions of polarized dielectrics.
Similarly, for the magnetostatic model in free space it is necessary to define only a single magnetic flux density vector B by specifying its divergence and its curl as postulates; all other formulas can be derived from these two postulates. Relations in material media can be developed through the concept of equivalent current densities. Of course, the validity of the postulates lies in their ability to yield results that conform with experimental evidence.
For time-varying fields, the electric and magnetic field intensities are coupled. The curl E postulate for the electrostatic model must be modified to conform with Faraday's law. In addition, the curl B postulate for the magnetostatic model must also be modified in order to be consistent with the equation of continuity. We have, then, the four Maxwell's equations that constitute the electromagnetic model. I believe that this gradual development of the electromagnetic model based on Helmholtz's theorem is novel, systematic, pedagogically sound, and more easily accepted by students.
A short Chapter 1 of the book provides some motivations for the study of electromagnetism. It also introduces the source functions, the fundamental field quantities, and the three universal constants for free space in the electromagnetic model. Chapter 2 reviews the basics of vector algebra, vector calculus, and the relations of Cartesian, cylindrical, and spherical coordinate systems. Chapter 3 develops the governing laws and methods of solution of electrostatic problems. Chapter 4 is on steady electric current fields and resistance calculations. Chapter 5 deals with static magnetic fields. Chapter 6, on time-varying electromagnetic fields, starts with Faraday's law of electromagnetic induction, and leads to Maxwell's equations and wave equations. The characteristics of plane electromagnetic waves are treated in Chapter 7. The theory and application s of transmission lines are studied in Chapter 8. Further engineering applications of electromagnetic fields and waves are discussed in Chapter 9 (waveguides and cavity resonators) and Chapter 10 (antennas, antenna arrays, and radar systems). Much of the material has been adapted and reduced from my larger book, Field and Wave Electromagnetics, but in this book I have incorporated a number of innovative pedagogical features.
Each chapter of this book starts with an overview section that provides qualitative guidance to the topics to be discussed in the chapter. Throughout the book worked-out examples follow important formulas and quantitative relations to illustrate methods for solving typical problems. Where appropriate, simple exercises with answers are included to test students' ability to handle related situations. At irregular intervals, a group of review questions are inserted after several related sections. These questions serve to provide an immediate feedback of the topics just discussed and to reinforce students' qualitative understanding of the material. Also, a number of pertinent remarks usually follow the review questions. These remarks contain some points of special importance that the students may have overlooked. When new definitions, concepts, or relations are introduced, short notes are added in the margins to emphasize their significance. At the end of each chapter there is a summary with bulleted items summarizing the main topics covered in the chapter. I hope that these pedagogical aids will prove to be useful in helping students learn electromagentics and its applications.
Many dedicated people, besides the author, are involved in the publication of a book such as this one. I wish to acknowledge the interest and support of Senior Editor Eileen Bernadette Moran and Executive Editor Don Fowley since the inception of this project. I also wish to express my appreciation to Production Supervisor Helen Wythe for her friendly assistance in keeping the production on schedule, as well as to Roberta Lewis, Amy Willcutt, Laura Michaels, and Alena Konecny for their contributions. Jim and Rosa Sullivan of Tech-Graphics were responsible for the illustrations. To them I offer my appreciation for their fine work. Above all, I wish to thank my wife, Enid, for her patience, understanding and encouragement through all phases of my challenging task of completing this book.
D.K.C.
The Electromagnetic Model | |
Overview | |
The electromagnetic model | |
SI units and universal constants | |
Summary | |
Vector Analysis | |
Overview | |
Vector addition and subtraction | |
Vector multiplication | |
Orthogonal coordinate systems | |
Gradient of a scalar field | |
Divergence of a vector field | |
Divergence theorem | |
Curl of a vector field | |
Stoke's theorem | |
Two null identities | |
Field classification and Helmholtz's theorem | |
Summary | |
Problems | |
Static Electric Fields | |
Overview | |
Fundamental postulates of electrostatics in free space | |
Coulomb's law | |
Gauss's law and applications | |
Electric potential | |
Material media in static electric field | |
Electric flux density and dielectric constant | |
Boundary conditions for electrostatic fields | |
Capacitances and capacitors | |
Electrostatic energy and forces | |
Solution of electrostatic boundary-value problems | |
Summary | |
Problems | |
Steady Electric Currents | |
Overview | |
Current density and Ohm's law | |
Equation of continuity and Kirchoff's current law | |
Power dissipation and Joule's law | |
Governing equations for steady current density | |
Resistance calculations | |
Summary | |
Problems | |
Static Magnetic Fields | |
Overview | |
Fundamental postulates of magnetostatics in free space | |
Vector magnetic potential | |
The Biot-Savart law and applications | |
The magnetic dipole | |
Magnetization and equivalent current densities | |
Magnetic field intensity and relative permeability | |
Behavior of magnetic materials | |
Boundary conditions for magnetostatic fields | |
Inductances and inductors | |
Magnetic energy | |
Magnetic forces and torques | |
Summary | |
Problems | |
Time-Varying Fields and Maxwell's Equations | |
Overview | |
Faraday's law of electromagnetic induction | |
Maxwell's equations | |
Potential functions | |
Time-harmonic fields | |
Summary | |
Problems | |
Plane Electromagnetic Waves | |
Overview | |
Plane waves in lossless media | |
Plane waves in lossy media | |
Group velocity | |
Flow of electromagentic power and the poynting vector | |
Normal incidence of plane waves at plane boundaries | |
Oblique incidence of plane waves at plane boundaries | |
Summary | |
Problems | |
Transmission Lines | |
Overview | |
General transmission-line equations | |
Transmission-line parameters | |
Wave characteristics on an infinite transmission line | |
Wave characteristics on finite transmission lines | |
The Smith chart | |
Transmission-line impedance matching | |
Summary | |
Problems | |
Waveguides and Cavity Resonators | |
Overview | |
General wave behaviors along uniform guiding structures | |
Rectrangular waveguides | |
Other waveguide types | |
Cavity resonators | |
Summary | |
Problems | |
Antennas and Antenna Arrays | |
Overview | |
The elemental electric dipole | |
Antenna patterns and directivity | |
Thin linear antennas | |
Antenna arrays | |
Effective area and backscatter cross section | |
Friis transmission formula and radar equation | |
Summary | |
Problems | |
Symbols and Units | |
Some Useful Material Constants | |
Bibliography | |
Answers to Odd-numbered Problems | |
Index | |
Back Endpapers | |
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