INTRODUCTORY ELECTROMAGNETICS Herbert P.Neff,Jr. University of Tennessee 國 WILEY JOHN WILEY SONS New York·Chichester·Brisbane·Toronto·Singapore
Copyright 1991.by John Wiley Sons,Inc. All rights reserved.Published simultaneouslyn Canada Reproduction or translation of any part of this work beyond that permitted by Sections owner is un on sho iohn Wiley Sons. Library of Congress Cataloging in Publication Data: Neff,Herbert P.,1930- Includes i ISBN0-471-60550.6 Electrical engineering.2.Electromagnetic fields.I.Title. TK145.N4151991 621.3-dc20 89-36373 CIP Printed in Singapore 10987654321
VECTOR RELATIONS UNIT VECTORS a,.a.a:-rectangular (constant) ap.a.a-cylindrical (nonconstant.except a.) ar.an.a-spherical (nonconstant) COORDINATE TRANSFORMATIONS x=pcos中=rsincosb y=psinΦ=rsin6sin中 =r cos 0 p=√x2+y2=r sin 中=tan-lylx r=2+2+2=八p+2 0=tan(+)=tan(p/) COORDINATE COMPONENT TRANSFORMATIONS A,=Ap cos中-A6sinb -A,sin cos中+An cos9cos中-Ao sin =A,sin0sin中+Ae cos0sin中+A6cos中 A:Ar cos 0-Ao sin 0 Ap=Ax cos +A,sin =Ar sin 0 Ae cos 6 Ab=-Ax sin中+Ay cos A,=Ax sin9cos中+A,sin0sin中+A-cos8 =Apsin A:cos A=A:cos 0 cos A:cos 0 sin -A:sin 0 =Apcos 0-A:sin 0 DIFFERENTIAL ELEMENTS OF VECTOR LENGTH [a dx +ay dy +a:dz dl= apdp+a6pd地+ad a,dr+agrd+aor sin9d中
DIFFERENTIAL ELEMENTS OF VECTOR AREA ax dy dz ay dx dz +a:dx dy dz +as dp dz a:pdpdd (a,r2sin6d0dΦ+aor sindrd地+aer dr d6 DIFFERENTIAL ELEMENTS OF VOLUME [dx dy dz r2 sin e dr d0dΦ VECTOR OPERATIONS-RECTANGULAR COORDINATES a=职++器 A映+的+赞 xA的}映-+监-0】 a-0+经+贤-pa 2A=a,2Ax+a,2A,+a,72A:=V(T·A)-V×(T×A) VECTOR OPERATIONS-CYLINDRICAL COORDINATES da 1da da Vo-a 口A=10 -品小+装+验 p0φ a++ =-剖++路+aA
ABOUT THE AUTHOR Herbert P.Neff,Jr.,received his bachelor's and master's degrees in electrical engineering from the University of Tennessee at Knoxville in 1953 and 1956 respectively.He received his doctorate in electrical engineering from Auburn University in 1967.From 1956 to 1965 and from 1966 to the present he has taught courses primarily in electromagnetics at the University of Tennessee.He is also a consultant to Oak Ridge National Laboratory. Dr.Neff has written four engineering textbooks and is the author or coauthor of numerous articles that have been published in professional journals.He is a member of Eta Kappa Nu,Sigma Xi.and Tau Beta Pi.He is a senior member of the Institute of Electrical and Electronics Engineers
PREFACE This text is written for a first semester junior level course in electromagnetics.The first chapter covers the basics of vector analysis,including the divergence,curl,and gradient operations.There are those who believe that the study of electromagnetics should begin with the static case (Chapter 2)allowing the student to gradually digest the material,whereas others (not including the author)believe that it is desirable to begin with the dynamic case (Chapter 3).Since all of the essentials of vector analysis are included in Chapter 1,this textbook allows the instructor to skip Chapter 2(with the possible exception of Section 2.15)if desired.This approach allows more material to be covered toward the end of the texthook. Chapter 2 includes electrostatics and magnetostatics.Although it certainly could be divided into two chapters,it was decided that,if combined,the topics could be covered in a shorter period of time.Something has to be reduced,in a one semester course,and this material is an obvious candidate.As indicated in the preceding paragraph,Chapter 3 begins with the dynamic case(Maxwell's general equations).The treatment here is a standard one,and there are few topics that can omitted. The material in Chapter 4 is important for several reasons.First,uniform plane waves represent a relatively simple application of Maxwell's equations from the preceding chapter.Second,the reflection of plane waves from surfaces,such as the earth,is an important consideration on its own.The behavior of uniform plane aves isvery similar to that of the fieds (Chapter 5) &aeesieonwnaicohoemae rectangular waveguide and the dielectric slab waveguide that appear in Chapter 6. The reader who is familiar with Basic Electromagnetic Fields,my textbook that is designed for a two-quarter course,will recognize much of the material from that textbook in Chapters 4,5,and 6 of this textbook. Chapter 5 is a rather typical treatment of transmission lines.It begins with the lossless case so that the general case (beginning with Section 5.14)can be omitted if desired,or if time requires that some material be skipped.The same general things can be said for Chapter 6 with regard to waveguides,and Section 6.8 dealing with losses,can be omitted Radiation is ordinarily the last topic covered in material of this type.Since it is expected(based on past experience)that this material cannot be covered because of
v PREFACE time limitations in a one semester course,it was decided that a full chapter would not be devoted to it.Instead,Appendix D is devoted to the basics of radiation includinga brief treatment of the ipole and.ftme allows,this material can be utilized. A first semester course in electromagnetics (for which this textbook would be appropriate)ofen appears with a course in basic linear system analysis where the unit-impulse function would normally first appear.In this circumstance the student would not be familiar with the use of this function,and, for this reason,it does not appear in this textbook.This is in contrast to Basic Electromagnetic Fields,where the unit-impulse function is used in several places to verify fundamental relations or to equate superposition and convolution integrals. It is obvious from the preceding considerations that this text could be used in a two-quarter scheme with very little material omitted.It is believed that Basic Electromagneric Fields would be more suitable for a two-semester or three quarter scheme.A suggested timetable for a one-semester course is outlined below (assuming a 15-week semester). Chapter 1 2 weeks Chapter 2 4 weeks Chapter 3 2 weeks Chapter 4 2 weeks Chapter 5 3 weeks Chapter 6 2 weeks Vector relations are conveniently summarized on the inside front and back covers for convenience.The symbols and units (MKSA)are the same as those listed following this preface.Answers to selected problems are listed following the appendixes.Problems at the end of the chapters that are somewhat more difficult are marked with an asterisk I express my sincere thanks to those reviewers and others whose suggestions have contributed to this textbook.In particular,I thank Professors Leonard Taylor, Matthew Sadiku,Randy Jost,and Kondagunta Sivaprasad.The typing of the original manuscript for this textbook was done by Roberta Campbell,and she is due much praise for her fine work. HERBERT P.NEFF,JR
CONTENTS CHAPTER 1 VECTOR ANALYSIS 1 1.1 Vector Addition I 1.2 Vector Multiplication 2 1.3 Coordinate Systems 4 1.4 Circulation and Flux 9 1.5 Divergence 13 1.6 Gradient 17 1.7 Curl 20 1.8 Some Fundamental Vector Identities 24 1.9 The Divergence Theorem 26 1.10 Stokes'Theorem 28 1.11 Concluding Remarks 30 CHAPTER 2 ELECTROSTATIC AND MAGNETOSTATIC FIELDS 34 2.1 Charge Configurations 35 2.2 Coulomb's Law and Electric Field Intensity 37 2.3 The Electrostatic Potential Field 47 2.4 Gauss's Law 53 2.5 Dielectrics 56 2.6 Poisson and Laplace Equations 61 2.7 Image Theory 67 2.8 Electric Current and Conservation of Charge 69 2.9 The Biot-Savart Law and Magnetic Field Intensity 72 2.10 Ampere's Circuital Law 80 2.11 Ampere's Law in Point Form(Maxwell's Equation)85
CONTENTS 2.12 Magnetic Scalar and Vector Potential 87 2.13 Magnetic Materials 91 2.14 Force and Torque 100 2.15 Capacitance,Resistance,and Inductance 102 2.16 Concluding Remarks 111 CHAPTER 3 MAXWELL'S EQUATIONS 126 3.1 Conservation of Charge 126 3.2 Other Field Quantities 128 3.3 Faraday's Law 130 3.4 Maxwell's Second Equation 137 3.5 A Summary of Maxwell's Equations 140 3.6 Poynting's Theorem 143 3.7 Potentials 150 3.8 Voltage and Potential Difference 159 3.9 Boundary Conditions 159 3.10 Circuit Theory from Field Theory 162 3.11 Concluding Remarks 165 CHAPTER 4 UNIFORM PLANE WAVE PROPAGATION 171 4.1 The Undamped Uniform Plane Wave 172 4.2 Wavelength and Phase Velocity 178 4.3 Power Density and Velocity of Energy Flow 179 4.4 Wave Impedance 180 4.5 Uniform Damped Plane Waves 183 4.6 Reflection of Plane Waves,Normal Incidence 187 4.7 Oblique Incidence 205 4.8 Polarization 217 4.9 Dispersion 220 4.10 Concluding Remarks 220 CHAPTER 5 TRANSMISSION LINES:TEM MODES 228 5.1 The Parallel Plane Guiding System 228 5.2 The General Lossless Line 230 5.3 The Lossless Line Equivalent Circuit 234
CONTENTS 5.4 General Solutions for V and /-Lossless Line 238 5.5 Voltage Standing Wave Ratio 243 5.6 Input Impedance 244 5.7 Special Load Impedances 246 5.8 Transmission Parameters 252 5.9 Multiple Loads 254 5.10 Transmission Line Measurements 256 5.11 The Smith Chart 257 5.12 Transmission Line Matching 268 5.13 Pulses on the Lossless Line 278 5.14 Losses 281 5.15 Special Two-Wire Lines 287 5.16 Quality Factor 290 5.17 Distributed Parameters 299 5.18 The Coaxial Cavity 302 5.19 Concluding Remarks 307 CHAPTER 6 WAVEGUIDES AND CAVITIES 317 6.1 The Rectangular Waveguide,TEo Mode 317 6.2 Properties of the TEo Mode 320 6.3 Waveguide Current,TEo Mode 329 6.4 Waveguide Vector Potentials 334 6.5 The Rectangular Waveguide,Higher Order Modes 337 6.6 Dielectric Waveguides 345 6.7 Lossless Cavity Resonators 355 6.8 Waveguide and Cavity Losses 358 6.9 Concluding Remarks 366 APPENDIX A PHYSICAL CONSTANTS 372 APPENDIX B MATERIAL PARAMETERS 373 APPENDIX C SPECIAL FUNCTIONS 375 APPENDIX D RADIATION 388 SYMBOLS AND UNITS 396 ANSWERS TO SELECTED PROBLEMS 401 INDEX 409