Engineering Electromagnetics – 8th Edition – William H. Hayt (1) PDF

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This page intentionally left blank Physical Constants Quantity Value Electron charge e = (1.602 177 33 ± 0.000 000 46) × 10−19 C Material S/m Material S/m Electron mass m = (9.109 389 7 ± 0.000 005 4) × 10−31 kg Permittivity of free space �0 = 8.854 187 817 × 10−12 F/m Permeability of free space µ0...

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Physical Constants

Quantity

Value

Electron charge Electron mass Permittivity of free space Permeability of free space Velocity of light

e = (1.602 177 33 ± 0.000 000 46) × 10−19 C m = (9.109 389 7 ± 0.000 005 4) × 10−31 kg �0 = 8.854 187 817 × 10−12 F/m µ0 = 4π 10−7 H/m c = 2.997 924 58 × 108 m/s

Material

S/m

Material

S/m

Dielectric Constant (�r� ) and Loss Tangent (� �� /� � )

Material Air Alcohol, ethyl Aluminum oxide Amber Bakelite Barium titanate Carbon dioxide Ferrite (NiZn) Germanium Glass Ice Mica Neoprene Nylon Paper Plexiglas Polyethylene Polypropylene Polystyrene Porcelain (dry process) Pyranol Pyrex glass Quartz (fused) Rubber Silica or SiO2 (fused) Silicon Snow Sodium chloride Soil (dry) Steatite Styrofoam Teflon Titanium dioxide Water (distilled) Water (sea) Water (dehydrated) Wood (dry)

ǫ�r 1.0005 25 8.8 2.7 4.74 1200 1.001 12.4 16 4–7 4.2 5.4 6.6 3.5 3 3.45 2.26 2.25 2.56 6 4.4 4 3.8 2.5–3 3.8 11.8 3.3 5.9 2.8 5.8 1.03 2.1 100 80 1 1.5–4

ǫ�� /ǫ� 0.1 0.000 6 0.002 0.022 0.013 0.000 25 0.002 0.05 0.000 6 0.011 0.02 0.008 0.03 0.000 2 0.000 3 0.000 05 0.014 0.000 5 0.000 6 0.000 75 0.002 0.000 75 0.5 0.000 1 0.05 0.003 0.000 1 0.000 3 0.001 5 0.04 4 0 0.01

Material

r

Material

r

Quantity

Value

Conductivity (� )

e m

Material

c

Material

r

Silver Copper Gold Aluminum Tungsten Zinc Brass Nickel Iron Phosphor bronze Solder Carbon steel German silver Manganin Constantan Germanium Stainless steel

ǫ , S/m 6.17 × 107 5.80 × 107 4.10 × 107 3.82 × 107 1.82 × 107 1.67 × 107 1.5 × 107 1.45 × 107 1.03 × 107 1 × 107 0.7 × 107 0.6 × 107 0.3 × 107 0.227 × 107 0.226 × 107 0.22 × 107 0.11 × 107

Material Nichrome Graphite Silicon Ferrite (typical) Water (sea) Limestone Clay Water (fresh) Water (distilled) Soil (sandy) Granite Marble Bakelite Porcelain (dry process) Diamond Polystyrene Quartz

ǫ , S/m 0.1 × 107 7 × 104 2300 100 5 −2 10 5 × 10−3 10−3 10−4 10−5 10−6 10−8 10−9 10−10 2 × 10−13 10−16 10−17

Relative Permeability (µr )

Material Bismuth Paraffin Wood Silver Aluminum Beryllium Nickel chloride Manganese sulfate Nickel Cast iron Cobalt

µr 0.999 998 6 0.999 999 42 0.999 999 5 0.999 999 81 1.000 000 65 1.000 000 79 1.000 04 1.000 1 50 60 60

Material Powdered iron Machine steel Ferrite (typical) Permalloy 45 Transformer iron Silicon iron Iron (pure) Mumetal Sendust Supermalloy

µr 100 300 1000 2500 3000 3500 4000 20 000 30 000 100 000

Engineering Electromagnetics EIGH T H E D I T I O N

William H. Hayt, Jr. Late Emeritus Professor Purdue University

John A. Buck

Georgia Institute of Technology

ENGINEERING ELECTROMAGNETICS, EIGHTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the C 2012 by The McGraw-Hill Companies, Inc. All rights Americas, New York, NY 10020. Copyright
C 2006, 2001, and 1989. No part of this publication may be reproduced or reserved. Previous editions
distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOC/DOC 1 0 9 8 7 6 5 4 3 2 1 ISBN 978-0-07-338066-7 MHID 0-07-338066-0 Vice President & Editor-in-Chief: Marty Lange Vice President EDP/Central Publishing Services: Kimberly Meriwether David Publisher: Raghothaman Srinivasan Senior Sponsoring Editor: Peter E. Massar Senior Marketing Manager: Curt Reynolds Developmental Editor: Darlene M. Schueller Project Manager: Robin A. Reed Design Coordinator: Brenda A. Rolwes Cover Design and Image: Diana Fouts Buyer: Kara Kudronowicz Media Project Manager: Balaji Sundararaman Compositor: Glyph International Typeface: 10.5/12 Times Roman Printer: R.R. Donnelley All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. Library of Congress Cataloging-in-Publication Data

Hayt, William Hart, 1920– Engineering electromagnetics / William H. Hayt, Jr., John A. Buck. — 8th ed. p. cm. Includes bibliographical references and index. ISBN 978–0–07–338066–7 (alk. paper) 1. Electromagnetic theory. I. Buck, John A. II. Title. QC670.H39 2010 530.14′ 1—dc22 2010048332

www.mhhe.com

To Amanda and Olivia

ABOUT THE AUTHORS

William H. Hayt. Jr. (deceased) received his B.S. and M.S. degrees at Purdue University and his Ph.D. from the University of Illinois. After spending four years in industry, Professor Hayt joined the faculty of Purdue University, where he served as professor and head of the School of Electrical Engineering, and as professor emeritus after retiring in 1986. Professor Hayt’s professional society memberships included Eta Kappa Nu, Tau Beta Pi, Sigma Xi, Sigma Delta Chi, Fellow of IEEE, ASEE, and NAEB. While at Purdue, he received numerous teaching awards, including the university’s Best Teacher Award. He is also listed in Purdue’s Book of Great Teachers, a permanent wall display in the Purdue Memorial Union, dedicated on April 23, 1999. The book bears the names of the inaugural group of 225 faculty members, past and present, who have devoted their lives to excellence in teaching and scholarship. They were chosen by their students and their peers as Purdue’s finest educators.

A native of Los Angeles, California, John A. Buck received his M.S. and Ph.D. degrees in Electrical Engineering from the University of California at Berkeley in 1977 and 1982, and his B.S. in Engineering from UCLA in 1975. In 1982, he joined the faculty of the School of Electrical and Computer Engineering at Georgia Tech, where he has remained for the past 28 years. His research areas and publications have centered within the fields of ultrafast switching, nonlinear optics, and optical fiber communications. He is the author of the graduate text Fundamentals of Optical Fibers (Wiley Interscience), which is now in its second edition. Awards include three institute teaching awards and the IEEE Third Millenium Medal. When not glued to his computer or confined to the lab, Dr. Buck enjoys music, hiking, and photography.

BRIEF CONTENTS

Preface xii

1 Vector Analysis 1 2 Coulomb’s Law and Electric Field Intensity 26 3 Electric Flux Density, Gauss’s Law, and Divergence

48

4 Energy and Potential 75 5 Conductors and Dielectrics 109 6 Capacitance 143 7 The Steady Magnetic Field 180 8 Magnetic Forces, Materials, and Inductance 230 9 Time-Varying Fields and Maxwell’s Equations 277 10 Transmission Lines 301 11 The Uniform Plane Wave 367 12 Plane Wave Reflection and Dispersion 406 13 Guided Waves 453 14 Electromagnetic Radiation and Antennas 511 Appendix A Vector Analysis 553 Appendix B Units 557 Appendix C Material Constants 562 Appendix D The Uniqueness Theorem 565 Appendix E Origins of the Complex Permittivity 567 Appendix F Answers to Odd-Numbered Problems 574 Index 580

v

CONTENTS

Chapter 3 Electric Flux Density, Gauss’s Law, and Divergence 48

Preface xii

Chapter 1 Vector Analysis

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Scalars and Vectors 1 Vector Algebra 2 The Rectangular Coordinate System 3 Vector Components and Unit Vectors 5 The Vector Field 8 The Dot Product 9 The Cross Product 11 Other Coordinate Systems: Circular Cylindrical Coordinates 13 1.9 The Spherical Coordinate System 18 References 22 Chapter 1 Problems 22

Chapter 2 Coulomb’s Law and Electric Field Intensity 26 2.1 The Experimental Law of Coulomb 26 2.2 Electric Field Intensity 29 2.3 Field Arising from a Continuous Volume Charge Distribution 33 2.4 Field of a Line Charge 35 2.5 Field of a Sheet of Charge 39 2.6 Streamlines and Sketches of Fields 41 References 44 Chapter 2 Problems 44

vi

3.1 Electric Flux Density 48 3.2 Gauss’s Law 52 3.3 Application of Gauss’s Law: Some Symmetrical Charge Distributions 56 3.4 Application of Gauss’s Law: Differential Volume Element 61 3.5 Divergence and Maxwell’s First Equation 64 3.6 The Vector Operator ∇ and the Divergence Theorem 67 References 70 Chapter 3 Problems 71

Chapter 4 Energy and Potential 75 4.1 Energy Expended in Moving a Point Charge in an Electric Field 76 4.2 The Line Integral 77 4.3 Definition of Potential Difference and Potential 82 4.4 The Potential Field of a Point Charge 84 4.5 The Potential Field of a System of Charges: Conservative Property 86 4.6 Potential Gradient 90 4.7 The Electric Dipole 95 4.8 Energy Density in the Electrostatic Field 100 References 104 Chapter 4 Problems 105

Contents

Chapter 5 Conductors and Dielectrics 109 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

Current and Current Density 110 Continuity of Current 111 Metallic Conductors 114 Conductor Properties and Boundary Conditions 119 The Method of Images 124 Semiconductors 126 The Nature of Dielectric Materials 127 Boundary Conditions for Perfect Dielectric Materials 133 References 137 Chapter 5 Problems 138

Chapter 6 Capacitance 143 6.1 6.2 6.3 6.4 6.5

Capacitance Defined 143 Parallel-Plate Capacitor 145 Several Capacitance Examples 147 Capacitance of a Two-Wire Line 150 Using Field Sketches to Estimate Capacitance in Two-Dimensional Problems 154 6.6 Poisson’s and Laplace’s Equations 160 6.7 Examples of the Solution of Laplace’s Equation 162 6.8 Example of the Solution of Poisson’s Equation: the p-n Junction Capacitance 169 References 172 Chapter 6 Problems 173

Chapter 7 The Steady Magnetic Field 180 7.1 Biot-Savart Law 180 7.2 Amp`ere’s Circuital Law 188 7.3 Curl 195

vii

7.4 Stokes’ Theorem 202 7.5 Magnetic Flux and Magnetic Flux Density 207 7.6 The Scalar and Vector Magnetic Potentials 210 7.7 Derivation of the Steady-Magnetic-Field Laws 217 References 223 Chapter 7 Problems 223

Chapter 8 Magnetic Forces, Materials, and Inductance 230 8.1 Force on a Moving Charge 230 8.2 Force on a Differential Current Element 232 8.3 Force between Differential Current Elements 236 8.4 Force and Torque on a Closed Circuit 238 8.5 The Nature of Magnetic Materials 244 8.6 Magnetization and Permeability 247 8.7 Magnetic Boundary Conditions 252 8.8 The Magnetic Circuit 255 8.9 Potential Energy and Forces on Magnetic Materials 261 8.10 Inductance and Mutual Inductance 263 References 270 Chapter 8 Problems 270

Chapter 9 Time-Varying Fields and Maxwell’s Equations 277 9.1 9.2 9.3 9.4 9.5

Faraday’s Law 277 Displacement Current 284 Maxwell’s Equations in Point Form 288 Maxwell’s Equations in Integral Form 290 The Retarded Potentials 292 References 296 Chapter 9 Problems 296

viii

Contents

Chapter 10 Transmission Lines

301

10.1 Physical Description of Transmission Line Propagation 302 10.2 The Transmission Line Equations 304 10.3 Lossless Propagation 306 10.4 Lossless Propagation of Sinusoidal Voltages 309 10.5 Complex Analysis of Sinusoidal Waves 311 10.6 Transmission Line Equations and Their Solutions in Phasor Form 313 10.7 Low-Loss Propagation 315 10.8 Power Transmission and The Use of Decibels in Loss Characterization 317 10.9 Wave Reflection at Discontinuities 320 10.10 Voltage Standing Wave Ratio 323 10.11 Transmission Lines of Finite Length 327 10.12 Some Transmission Line Examples 330 10.13 Graphical Methods: The Smith Chart 334 10.14 Transient Analysis 345 References 358 Chapter 10 Problems 358

Chapter 11 The Uniform Plane Wave 367 11.1 11.2 11.3 11.4

Wave Propagation in Free Space 367 Wave Propagation in Dielectrics 375 Poynting’s Theorem and Wave Power 384 Propagation in Good Conductors: Skin Effect 387 11.5 Wave Polarization 394 References 401 Chapter 11 Problems 401

Chapter 12 Plane Wave Reflection and Dispersion 406 12.1 Reflection of Uniform Plane Waves at Normal Incidence 406 12.2 Standing Wave Ratio 413

12.3 Wave Reflection from Multiple Interfaces 417 12.4 Plane Wave Propagation in General Directions 425 12.5 Plane Wave Reflection at Oblique Incidence Angles 428 12.6 Total Reflection and Total Transmission of Obliquely Incident Waves 434 12.7 Wave Propagation in Dispersive Media 437 12.8 Pulse Broadening in Dispersive Media 443 References 447 Chapter 12 Problems 448

Chapter 13 Guided Waves 453 13.1 Transmission Line Fields and Primary Constants 453 13.2 Basic Waveguide Operation 463 13.3 Plane Wave Analysis of the Parallel-Plate Waveguide 467 13.4 Parallel-Plate Guide Analysis Using the Wave Equation 476 13.5 Rectangular Waveguides 479 13.6 Planar Dielectric Waveguides 490 13.7 Optical Fiber 496 References 506 Chapter 13 Problems 506

Chapter 14 Electromagnetic Radiation and Antennas 511 14.1 Basic Radiation Principles: The Hertzian Dipole 511 14.2 Antenna Specifications 518 14.3 Magnetic Dipole 523 14.4 Thin Wire Antennas 525 14.5 Arrays of Two Elements 533 14.6 Uniform Linear Arrays 537 14.7 Antennas as Receivers 541 References 548 Chapter 14 Problems 548

ix

Contents

Appendix A Vector Analysis A.1 A.2 A.3

553

General Curvilinear Coordinates 553 Divergence, Gradient, and Curl in General Curvilinear Coordinates 554 Vector Identities 556

Appendix D The Uniqueness Theorem Appendix E Origins of the Complex Permittivity 567

Appendix B Units 557

Appendix F Answers to Odd-Numbered Problems 574

Appendix C Material Constants 562

Index 580

565

PREFACE

It has been 52 years since the first edition of this book was published, then under the sole authorship of William H. Hayt, Jr. As I was five years old at that time, this would have meant little to me. But everything changed 15 years later when I used the second edition in a basic electromagnetics course as a college junior. I remember my sense of foreboding at the start of the course, being aware of friends’ horror stories. On first opening the book, however, I was pleasantly surprised by the friendly writing style and by the measured approach to the subject, which — at least for me — made it a very readable book, out of which I was able to learn with little help from my professor. I referred to it often while in graduate school, taught from the fourth and fifth editions as a faculty member, and then became coauthor for the sixth and seventh editions on the retirement (and subsequent untimely death) of Bill Hayt. The memories of my time as a beginner are clear, and I have tried to maintain the accessible style that I found so welcome then. Over the 50-year span, the subject matter has not changed, but emphases have. In the universities, the trend continues toward reducing electrical engineering core course allocations to electromagnetics. I have made efforts to streamline the presentation in this new edition to enable the student to get to Maxwell’s equations sooner, and I have added more advanced material. Many of the earlier chapters are now slightly shorter than their counterparts in the seventh edition. This has been done by economizing on the wording, shortening many sections, or by removing some entirely. In some cases, deleted topics have been converted to stand-alone articles and moved to the website, from which they can be downloaded. Major changes include the following: (1) The material on dielectrics, formerly in Chapter 6, has been moved to the end of Chapter 5. (2) The chapter on Poisson’s and Laplace’s equations has been eliminated, retaining only the one-dimensional treatment, which has been moved to the end of Chapter 6. The two-dimensional Laplace equation discussion and that of numerical methods have been moved to the website for the book. (3) The treatment on rectangular waveguides (Chapter 13) has been expanded, presenting the methodology of two-dimensional boundary value problems in that context. (4) The coverage of radiation and antennas has been greatly expanded and now forms the entire Chapter 14. Some 130 new problems have been added throughout. For some of these, I chose particularly good “classic” problems from the earliest editions. I have also adopted a new system in which the approximate level of difficulty is indicated beside each problem on a three-level scale. The lowest level is considered a fairly straightforward problem, requiring little work assuming the material is understood; a level 2 problem is conceptually more difficult, and/or may require more work to solve; a level 3 problem is considered either difficult conceptually, or may require extra effort (including possibly the help of a computer) to solve.

x

Preface

As in the previous edition, the transmission lines chapter (10) is stand-alone, and can be read or covered in any part of a course, including the beginning. In it, transmission lines are treated entirely within the context of circuit theory; wave phenomena are introduced and used exclusively in the form of voltages and currents. Inductance and capacitance concepts are treated as known parameters, and so there is no reliance on any other chapter. Field concepts and parameter computation in transmission lines appear in the early part of the waveguides chapter (13), where they play additional roles of helping to introduce waveguiding concepts. The chapters on electromagnetic waves, 11 and 12, retain their independence of transmission line theory in that one can progress from Chapter 9 directly to Chapter 11. By doing this, wave phenomena are introduced from first principles but within the context of the uniform plane wave. Chapter 11 refers to Chapter 10 in places where the latter may give additional perspective, along with a little more detail. Nevertheless, all necessary material to learn plane waves without previously studying transmission line waves is found in Chapter 11, should the student or instructor wish to proceed in that order. The new chapter on antennas covers radiation concepts, building on the retarded potential discussion in Chapter 9. The discussion focuses on the dipole antenna, individually and in simple arrays. The last section covers elementary transmit-receive systems, again using the dipole as a vehicle. The book is designed optimally for a two-semester course. As is evident, statics concepts are emphasized and occur first in the presentation, but again Chapter 10 (transmission lines) can be read first. In a single course that emphasizes dynamics, the transmission lines chapter can be covered initially as mentioned or at any point in the course. One way to cover the statics material more rapidly is by deemphasizing materials properties (assuming these are covered in other courses) and some of the advanced topics. This involves omitting Chapter 1 (assigned to be read as a review), and omitting Sections 2.5, 2.6, 4.7, 4.8, 5.5–5.7, 6.3, 6.4, 6.7, 7.6, 7.7, 8.5, 8.6, 8.8, 8.9, and 9.5. A supplement to this edition is web-based material consisting of the aforementioned articles on special topics in addition to animated demonstrations and interactive programs developed by Natalya Nikolova of McMaster University and Vikram Jandhyala of the University of Washington. Their excellent contributions are geared to the text, and icons appear in the margins whenever an exercise that pertains to the narrative exists. In addition, quizzes are provided to aid in further study. The theme of the text is the same as it has been since the first edition of 1958. An inductive approach is used th...