Revised First Edition Bassim Hamadeh, CEO and Publisher Michael Simpson, Vice President of Acquisitions Jamie Giganti, Senior Managing Editor Jess Busch, Senior Graphic Designer John Remington, Senior Field Acquisitions Editor Alexa Lucido, Licensing Coordinator Copyright © 2016 by Cognella, Inc. All rights reserved. No part of this publication may be reprinted, reproduced, transmitted, or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information retrieval system without the written permission of Cognella, Inc. First published in the United States of America in 2016 by Cognella, Inc. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Printed in the United States of America ISBN: 978-1-63487-949-1 (pbk)/ 978-1-63487-950-7 (br) BIOGRAPHIES Arlon T. Adams (PhD, University of Michigan) is Professor Emeritus of Electrical and Computer Engineering at Syracuse University, where he taught and did research in electromagnetics for many years, with research interests in antennas and microwaves. He served as electronics officer in the U. S. Navy and worked as an engineer for the Sperry Gyroscope Company. He is a Life Fellow of the IEEE from which institution he received eight prize-paper and achievement awards. He has been a Fullbright Scientist in Yugoslavia, a visiting scholar at Berkeley and was general chairman of the 1988 IEEE AP-S (Antennas and Propagation Society) /URSI International Symposium at Syracuse, New York. Jay Kyoon Lee (PhD, Massachusetts Institute of Technology) is Professor of Electrical Engineering and Computer Science at Syracuse University, where he teaches Electromagnetics, among other courses. His current research interests are electromagnetic theory, waves in anisotropic media, microwave remote sensing, antennas and propagation. He was a Research Fellow at Naval Air Development Center, Rome Air Development Center and Naval Research Laboratory and was an Invited Visiting Professor at Seoul National University in Seoul, Korea. He has received the Eta Kappa Nu Outstanding Undergraduate Teacher Award (1999), the IEEE Third Millennium Medal (2000), and the College Educator of the Year Award from the Technology Alliance of Central New York (2002). To Judtih Schettler Adams and Young Hee Kim Lee CONTENTS PREFACE XIII LIST OF TABLES 1 CHAPTER 1 Vector Analysis 2 1.1 INTRODUCTION 3 1.1.1 Josiah Willard Gibbs and the Development of Vector Analysis 3 1.2 VECTOR ALGEBRA 4 1.2.1 Basic Operations of Vector Algebra 4 1.2.2 Vector Algebra in Rectangular Coordinates 8 1.2.3 Triple Products 10 1.3 COORDINATE SYSTEMS 12 1.3.1 Coordinate System Geometry 12 1.3.2 Differential Elements of Length, Surface and Volume 14 1.3.3 Coordinate Transformations 17 1.3.4 Integrals of Vector Functions 21 1.4 VECTOR CALCULUS 27 1.4.1 Definitions 27 1.4.2 Gradient 29 1.4.3 Divergence 31 1.4.4 Curl 33 1.4.5 The Divergence Theorem and Stokes’ Theorem – Solenoidal and Conservative Fields 34 1.4.6 Vector Identities 42 1.4.7 Higher Order Functions of Vector Calculus 44 1.5 HELMHOLTZ’S THEOREM 45 PROBLEMS 47 CHAPTER 2 Electrostatic Fields and Potentials 60 2.1 INTRODUCTION 61 2.2 ELECTRIC CHARGE 61 2.3 THE ELECTRIC FIELD IN FREE SPACE 65 2.4 CHARLES AUGUSTIN COULOMB AND THE DISCOVERY OF COULOMB’S LAW 66 2.5 GAUSS’ LAW 70 2.6 THE ELECTRIC FIELDS OF ARBITRARY CHARGE DISTRIBUTIONS 77 2.7 THE SCALAR ELECTRIC POTENTIAL V 85 2.8 POTENTIAL OF AN ARBITRARY CHARGE DISTRIBUTION 87 2.9 CONDUCTORS 92 2.10 THE ELECTRIC DIPOLE 98 PROBLEMS 101 CHAPTER 3 Dielectrics 116 3.1 INTRODUCTION 117 3.2 POLARIZATION 117 3.3 THE ELECTRIC FIELD OF A POLARIZED DIELECTRIC 119 3.4 THE DISPLACEMENT VECTOR D 125 3.5 BOUNDARY CONDITIONS 131 3.6 CAPACITANCE 134 3.7 BENJAMIN FRANKLIN AND THE BEGINNINGS OF ELECTRIC SCIENCE 141 3.8 THE FORCE ON A CONDUCTOR IN ELECTRIC FIELD 144 3.9 ENERGY AND FORCES IN THE ELECTROSTATIC FIELD 146 3.9.1. Energy of a Collection of Point Charges 146 3.9.2. Energy of a Continuous Charge Distribution 148 3.9.3 Forces and Torques in Terms of Energy 151 PROBLEMS 153 CHAPTER 4 Special Solution Techniques 162 4.1 INTRODUCTION 163 4.2 LAPLACE’S AND POISSON’S EQUATIONS 163 4.2.1 Laplace’s Equation in One Dimension 164 4.2.2 Uniqueness Theorem 168 4.2.3 Marquis Pierre Simon de Laplace 169 4.3 METHOD OF IMAGES 170 4.3.1 A Point Charge Near a Grounded Conducting Plane 170 4.3.2 A Line Charge and a Parallel Conducting Cylinder 174 4.3.3 A Point Charge Near a Grounded Conducting Sphere 176 4.4 METHOD OF SEPARATION OF VARIABLES 177 4.4.1 Boundary Value Problems in Cartesian Coordinates 177 4.4.2 Boundary Value Problems in Cylindrical Coordinates 188 4.4.3 Boundary Value Problems in Spherical Coordinates 193 PROBLEMS 199 CHAPTER 5 Steady Currents and Conductive Materials 206 5.1 INTRODUCTION 207 5.2 ELECTRIC CURRENT 207 5.3 THE EQUATION OF CONTINUITY 209 5.4 OHM’S LAW AND CONDUCTIVE MATERIALS 211 5.5 GEORG SIMON OHM AND THE DISCOVERY OF OHM’S LAW 213 5.6 POWER – JOULE’S LAW 215 5.7 RELAXATION TIME 215 5.8 BOUNDARY CONDITIONS FOR STEADY CURRENTS 217 5.9 A RELATIONSHIP BETWEEN CAPACITANCE AND RESISTANCE 219 PROBLEMS 224 CHAPTER 6 Magnetostatic Fields 228 6.1 INTRODUCTION 229 6.2 MAGNETIC FIELD 229 6.3 BASIC LAWS OF MAGNETOSTATICS 231 6.4 AMPÈRE’S LAW 232 6.5 THE MAGNETIC VECTOR POTENTIAL AND THE BIOT-SAVART LAW 240 (THE MAGNETIC FIELDS OF ARBITRARY CURRENT DISTRIBUTIONS) 6.6 THE MAGNETIC DIPOLE 252 6.7 FORCES AND TORQUES ON CURRENTS IN MAGNETIC FIELDS 255 6.8 AMPÈRE’S FORCE LAW 260 6.9 A. M. AMPÈRE AND THE MAGNETIC FIELDS OF STEADY CURRENTS 261 6.10 THE HALL EFFECT 263 PROBLEMS 264 CHAPTER 7 Magnetostatic Fields in Matter 274 7.1 INTRODUCTION 275 7.2 MAGNETIZATION 276 7.3 THE MAGNETIC FIELD B OF A MAGNETIZED MATERIAL 277 7.4 THE MAGNETIC INTENSITY H 279 7.5 BOUNDARY CONDITIONS 285 7.6 INDUCTANCE 288 7.7 JOSEPH HENRY AND THE DISCOVERY OF MAGNETIC INDUCTION 295 7.8 MAGNETIC ENERGY 297 7.9 MAGNETIC FORCES AND TORQUES 301 7.10 MAGNETIC MATERIALS 303 PROBLEMS 306 CHAPTER 8 Time-Varying Fields: Faraday’s Law and Maxwell’s Equations 316 8.1 INTRODUCTION 317 8.2 LAWS OF ELECTROSTATICS AND MAGNETOSTATICS—A SUMMARY 317 8.3 FARADAY’S LAW 319 8.3.1 General Forms of Faraday’s Law 319 8.3.2 The Effects of Motion Through Magnetic Fields 321 8.3.3 Non-Relativistic Integral Forms of Faraday’s Law 323 8.3.4 Lenz’s Law 328 8.4 MICHAEL FARADAY’S FAMOUS EXPERIMENTS OF 1831 329 8.5 MAXWELL’S EQUATIONS 331 8.5.1 Displacement Current 332 8.5.2 Maxwell’s Equations 336 8.5.3 The Wave Equation—Electromagnetic Waves! 338 8.5.4 James Clerk Maxwell 340 8.6 BOUNDARY CONDITIONS FOR TIME-VARYING FIELDS 342 8.7 FLOW OF ELECTROMAGNETIC POWER: POYNTING’S THEOREM 344 PROBLEMS 348 CHAPTER 9 Electromagnetic Waves 356 9.1 INTRODUCTION 357 9.2. THE WAVE EQUATION IN A SOURCE-FREE REGION 357 9.2.1 One-Dimensional Wave Solutions 359 9.3. TIME-HARMONIC ELECTROMAGNETIC FIELDS 361 9.3.1 Phasor Representation of Time-Harmonic Fields 361 9.3.2 Maxwell’s Equations for Time-Harmonic Fields 363 9.3.3 Complex Poynting’s Theorem—Real Power Flow 364 9.4. UNIFORM PLANE WAVES IN LOSSLESS MEDIA 368 9.4.1 Uniform Plane Waves Propagating in Arbitrary Direction 376 9.5. UNIFORM PLANE WAVES IN LOSSY MEDIA 378 9.5.1 Attenuation of Waves 378 9.5.2 Good Dielectric vs. Good Conductor 382 9.6 DISPERSION OF WAVES—GROUP VELOCITY 387 9.7. POLARIZATION OF WAVES 390 PROBLEMS 394 CHAPTER 10 Reflection and Transmission of Waves 402 10.1 INTRODUCTION 403 10.2 NORMAL INCIDENCE AT A DIELECTRIC BOUNDARY 403 10.3 OBLIQUE INCIDENCE AT A DIELECTRIC BOUNDARY 408 10.3.1 Perpendicular Polarization 409 10.3.2 Parallel Polarization 414 10.4 TOTAL INTERNAL REFLECTION 421 10.5 BREWSTER ANGLE EFFECT 425 10.6 REFLECTION FROM PERFECT CONDUCTOR—STANDING WAVES 426 PROBLEMS 432 CHAPTER 11 Waveguides, Resonators, and Transmission Lines 440 11.1 INTRODUCTION 441 11.2 SOLUTION METHODS FOR UNIFORM WAVEGUIDES 442 11.3 PARALLEL PLATE WAVEGUIDE 446 11.3.1 TM Mode Solutions 447 11.3.2 TE Mode Solutions 452 11.4 RECTANGULAR WAVEGUIDE 458 11.4.1 General Field Solutions 459 11.4.2 TM Mode Solutions 460 11.4.3 TE Mode Solutions 465 11.5 RECTANGULAR CAVITY RESONATOR 470 11.5.1 TM Mode Solutions 471 11.5.2 TE Mode Solutions 473 11.5.3 Quality Factor of the Cavity Resonator 475 11.6 COAXIAL CABLE 477 11.6.1 TEM Mode Solutions 478 11.7 TRANSMISSION LINES 480 11.7.1 The Transmission-Line Equations—Lumped-Circuit Model 480 11.7.2 The Transmission-Line Equations from Field Theory 483 11.7.3 Transmission-Line Circuit Parameters 486 11.7.4 Finite Transmission Line with Load 489 PROBLEMS 493 CHAPTER 12 Radiation and Antennas 502 12.1 INTRODUCTION 503 12.2 POTENTIAL FORMULATION—METHOD OF SOLUTIONS FOR RADIATION PROBLEMS 503 12.2.1 Retarded Potentials 506 12.2.2 Retarded Vector Potential for Time-Harmonic Fields 507 12.2.3 Finding Antenna Fields 509 12.3 ELEMENTARY DIPOLE ANTENNA—HERTZIAN DIPOLE 510 12.3.1 Radiation Fields of a Hertzian Dipole 513 12.3.2 Near Fields of a Hertzian Dipole 516 12.4 LINEAR ANTENNA—LONG DIPOLE 519 12.4.1 Half-Wave Dipole 522 12.5 ANTENNA ARRAYS 524 12.5.1 Two-Element Array 524 12.5.2 Uniform Linear Array 528 PROBLEMS 532 BIBLIOGRAPHY 541 APPENDIX A 543 A-1 Physical Constants 543 A-2 Prefixes 543 A-3 Frequently Used Symbols and Their Units 544 APPENDIX B 545 Tables for Vector Analysis 545 ANSWERS TO SELECTED PROBLEMS 551 INDEX 561 PREFACE Electromagnetics is not an easy subject for students.