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Engineering Electromagnetics
Sixth Edition
William H. Hayt, Jr. . John A. Buck
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Engineering Electromagnetics
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Textbook Table of Contents
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McGraw-Hill Series in Electrical and Computer Engineering
SENIOR CONSULTING EDITOR
Stephen W. Director, University of Michigan, Ann Arbor
Circuits and Systems
Communications and Signal Processing
Computer Engineering
Control Theory and Robotics
Electromagnetics
Electronics and VLSI Circuits
Introductory
Power
Antennas, Microwaves, and Radar
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Previous Consulting Editors
Ronald N. Bracewell, Colin Cherry, James F. Gibbons, Willis W. Harman,
Hubert Heffner, Edward W. Herold, John G. Linvill, Simon Ramo, Ronald A.
Rohrer, Anthony E. Siegman, Charles Susskind, Frederick E. Terman, John G.
Truxal, Ernst Weber, and John R. Whinnery
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Engineering
Electromagnetics
SIXTH EDITION
William H. Hayt, Jr.
Late Emeritus Professor
Purdue University
John A. Buck
Georgia Institute of Technology
Burr Ridge, IL Dubuque, IA Madison, WI
New York San Francisco St. Louis
Bangkok Bogotá Caracas Lisbon London Madrid Mexico City
Milan New Delhi Seoul Singapore Sydney Taipei Toronto
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BRIEF CONTENTS
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Preface
xi
Vector Analysis
Coulomb's Law and Electric Field Intensity
Electric Flux Density, Gauss' Law, and Divergence
Energy and Potential
Conductors, Dielectrics, and Capacitance
Experimental Mapping Methods
Poisson's and Laplace's Equations
The Steady Magnetic Field
Magnetic Forces, Materials, and Inductance
Time-Varying Fields and Maxwell's Equations
The Uniform Plane Wave
Plane Waves at Boundaries and in Dispersive Media
Transmission Lines
Waveguide and Antenna Fundamentals
1
Appendix
Appendix
Appendix
Appendix
Appendix
Index
27
53
83
119
169
195
224
274
322
348
387
435
484
A Vector Analysis
529
B Units
534
C Material Constants
540
D Origins of the Complex Permittivity
E Answers to Selected Problems
544
551
To find Appendix E, please visit the expanded book website:
www.mhhe.com/engcs/electrical/haytbuck
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PREFACE
Over the years, I have developed a familiarity with this book in its various
editions, having learned from it, referred to it, and taught from it. The second
edition was used in my first electromagnetics course as a junior during the early
'70's. Its simple and easy-to-read style convinced me that this material could be
learned, and it helped to confirm my latent belief at the time that my specialty
would lie in this direction. Later, it was not surprising to see my own students
coming to me with heavily-marked copies, asking for help on the drill problems,
and taking a more active interest in the subject than I usually observed. So, when
approached to be the new co-author, and asked what I would do to change the
book, my initial feeling wasÐnothing. Further reflection brought to mind earlier
wishes for more material on waves and transmission lines. As a result, Chapters 1
to 10 are original, while 11 to 14 have been revised, and contain new material.
A conversation with Bill Hayt at the project's beginning promised the start
of what I thought would be a good working relationship. The rapport was
immediate. His declining health prevented his active participation, but we
seemed to be in general agreement on the approach to a revision. Although I
barely knew him, his death, occurring a short time later, deeply affected me in the
sense that someone that I greatly respected was gone, along with the promise of a
good friendship. My approach to the revision has been as if he were still here. In
the front of my mind was the wish to write and incorporate the new material in a
manner that he would have approved, and which would have been consistent
with the original objectives and theme of the text. Much more could have been
done, but at the risk of losing the book's identity and possibly its appeal.
Before their deaths, Bill Hayt and Jack Kemmerly completed an entirely
new set of drill problems and end-of-chapter problems for the existing material at
that time, up to and including the transmission lines chapter. These have been
incorporated, along with my own problems that pertain to the new topics. The
other revisions are summarized as follows: The original chapter on plane waves
has now become two. The first (Chapter 11) is concerned with the development
of the uniform plane wave and the treatment wave propagation in various media.
These include lossy materials, where propagation and loss are now modeled in a
general way using the complex permittivity. Conductive media are presented as
special cases, as are materials that exhibit electronic or molecular resonances. A
new appendix provides background on resonant media. A new section on wave
polarization is also included. Chapter 12 deals with wave reflection at single and
multiple interfaces, and at oblique incidence angles. An additional section on
dispersive media has been added, which introduces the concepts of group velocity and group dispersion. The effect of pulse broadening arising from group
dispersion is treated at an elementary level. Chapter 13 is essentially the old
transmission lines chapter, but with a new section on transients. Chapter 14 is
intended as an introduction to waveguides and antennas, in which the underlying
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PREFACE
physical concepts are emphasized. The waveguide sections are all new, but the
antennas treatment is that of the previous editions.
The approach taken in the new material, as was true in the original work, is
to emphasize physical understanding and problem-solving skills. I have also
moved the work more in the direction of communications-oriented material,
as this seemed a logical way in which the book could evolve, given the material
that was already there. The perspective has been broadened by an expanded
emphasis toward optics concepts and applications, which are presented along
with the more traditional lower-frequency discussions. This again seemed to be a
logical step, as the importance of optics and optical communications has
increased significantly since the earlier editions were published.
The theme of the text has not changed since the first edition of 1958. An
inductive approach is used that is consistent with the historical development. In
it, the experimental laws are presented as individual concepts that are later
unified in Maxwell's equations. Apart from the first chapter on vector analysis,
the mathematical tools are introduced in the text on an as-needed basis.
Throughout every edition, as well as this one, the primary goal has been to
enable students to learn independently. Numerous examples, drill problems
(usually having multiple parts), and end-of-chapter problems are provided to
facilitate this. Answers to the drill problems are given below each problem.
Answers to selected end-of-chapter problems can be found on the internet at
www.mhhe.com/engcs/electrical/haytbuck. A solutions manual is also available.
The book contains more than enough material for a one-semester course.
As is evident, statics concepts are emphasized and occur first in the presentation.
In a course that places more emphasis on dynamics, the later chapters can be
reached earlier by omitting some or all of the material in Chapters 6 and 7, as
well as the later sections of Chapter 8. The transmission line treatment (Chapter
13) relies heavily on the plane wave development in Chapters 11 and 12. A more
streamlined presentation of plane waves, leading to an earlier arrival at transmission lines, can be accomplished by omitting sections 11.5, 12.5, and 12.6. Chapter
14 is intended as an ``advanced topics'' chapter, in which the development of
waveguide and antenna concepts occurs through the application of the methods
learned in earlier chapters, thus helping to solidify that knowledge. It may also
serve as a bridge between the basic course and more advanced courses that
follow it.
I am deeply indebted to several people who provided much-needed feedback and assistance on the work. Glenn S. Smith, Georgia Tech, reviewed parts
of the manuscript and had many suggestions on the content and the philosophy
of the revision. Several outside reviewers pointed out errors and had excellent
suggestions for improving the presentation, most of which, within time limitations, were taken. These include Madeleine Andrawis, South Dakota State
University, M. Yousif El-Ibiary, University of Oklahoma, Joel T. Johnson,
Ohio State University, David Kelley, Pennsylvania State University, Sharad R.
Laxpati, University of Illinois at Chicago, Masoud Mostafavi, San Jose State
University, Vladimir A. Rakov, University of Florida, Hussain Al-Rizzo, Sultan
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PREFACE
Qaboos University, Juri Silmberg, Ryerson Polytechnic University and Robert
M. Weikle II, University of Virginia. My editors at McGraw-Hill, Catherine
Fields, Michelle Flomenhoft, and Betsy Jones, provided excellent expertise and
supportÐparticularly Michelle, who was almost in daily contact, and provided
immediate and knowledgeable answers to all questions and concerns. My seemingly odd conception of the cover illustration was brought into reality through
the graphics talents of Ms Diana Fouts at Georgia Tech. Finally, much is owed
to my wife and daughters for putting up with a part-time husband and father for
many a weekend.
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John A. Buck
Atlanta, 2000
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xiii
CONTENTS
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Preface
xi
Vector Analysis
1
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
1.8.
Scalars and Vectors
Vector Algebra
The Cartesian Coordinate System
Vector Components and Unit Vectors
The Vector Field
The Dot Product
The Cross Product
Other Coordinate Systems: Circular Cylindrical
Coordinates
1.9. The Spherical Coordinate System
2
3
4
6
9
10
13
Coulomb's Law and Electric Field Intensity
27
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
28
31
36
38
44
46
15
20
The Experimental Law of Coulomb
Electric Field Intensity
Field Due to a Continuous Volume Charge Distribution
Field of a Line Charge
Field of a Sheet Charge
Streamlines and Sketches of Fields
Electric Flux Density, Gauss' Law, and Divergence
53
3.1. Electric Flux Density
3.2. Gauss' Law
3.3. Applications of Gauss' Law: Some Symmetrical Charge
Distributions
3.4. Application of Gauss' Law: Differential Volume Element
3.5. Divergence
3.6. Maxwell's First Equation (Electrostatics)
3.7. The Vector Operator r and the Divergence Theorem
54
57
Energy and Potential
83
4.1. Energy and Potential in a Moving Point Charge in an
Electric Field
4.2. The Line Integral
4.3. De®nition of Potential Difference and Potential
4.4. The Potential Field of a Point Charge
84
85
91
93
62
67
70
73
74
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CONTENTS
Chapter 5
Chapter 6
Chapter 7
Chapter 8
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4.5. The Potential Field of a System of Charges: Conservative
Property
4.6. Potential Gradient
4.7. The Dipole
4.8. Energy Density in the Electric Field
95
99
106
110
Conductors, Dielectrics, and Capacitance
119
5.1. Current and Current Density
5.2. Continuity of Current
5.3. Metallic Conductors
5.4. Conductor Properties and Boundary Conditions
5.5. The Method of Images
5.6. Semiconductors
5.7. The Nature of Dielectric Materials
5.8. Boundary Conditions for Perfect Dielectric Materials
5.9. Capacitance
5.10. Several Capacitance Examples
5.11. Capacitance of a Two-Wire Line
120
122
124
129
134
136
138
144
150
154
157
Experimental Mapping Methods
169
6.1.
6.2.
6.3.
6.4.
170
176
183
186
Curvilinear Squares
The Iteration Method
Current Analogies
Physical Models
Poisson's and Laplace's Equations
195
7.1 Poisson's and Laplace's Equations
7.2. Uniqueness Theorem
7.3. Examples of the Solution of Laplace's Equation
7.4. Example of the Solution of Poisson's Equation
7.5. Product Solution of Laplace's Equation
196
198
200
207
211
The Steady Magnetic Field
224
8.1.
8.2.
8.3.
8.4.
8.5.
8.6.
8.7.
225
232
239
246
251
254
261
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Biot-Savart Law
Ampere's Circuital Law
Curl
Stokes' Theorem
Magnetic Flux and Magnetic Flux Density
The Scalar and Vector Magnetic Potentials
Derivation of the Steady-Magnetic-Field Laws
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CONTENTS
Chapter 9
Chapter 10
Chapter 11
Chapter 12
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274
9.1. Force on a Moving Charge
9.2. Force on a Differential Current Element
9.3. Force Between Differential Current Elements
9.4. Force and Torque on a Closed Circuit
9.5. The Nature of Magnetic Materials
9.6. Magnetization and Permeability
9.7. Magnetic Boundary Conditions
9.8. The Magnetic Circuit
9.9. Potential Energy and Forces on Magnetic Materials
9.10. Inductance and Mutual Inductance
275
276
280
283
288
292
297
299
306
308
Time-Varying Fields and Maxwell's Equations
322
10.1.
10.2.
10.3.
10.4.
10.5.
323
329
334
336
338
Faraday's Law
Displacement Current
Maxwell's Equations in Point Form
Maxwell's Equations in Integral Form
The Retarded Potentials
The Uniform Plane Wave
348
11.1.
11.2.
11.3.
11.4.
11.5.
348
356
365
369
376
Wave Propagation in Free Space
Wave Propagation in Dielectrics
The Poynting Vector and Power Considerations
Propagation in Good Conductors: Skin Effect
Wave Polarization
Plane Waves at Boundaries and in Dispersive Media
387
12.1.
12.2.
12.3.
12.4.
12.5.
12.6.
388
395
400
408
411
421
Re¯ection of Uniform Plane Waves at Normal Incidence
Standing Wave Ratio
Wave Re¯ection from Multiple Interfaces
Plane Wave Propagation in General Directions
Plane Wave Re¯ection at Oblique Incidence Angles
Wave Propagation in Dispersive Media
Transmission Lines
435
13.1.
13.2.
13.3.
13.4.
13.5.
13.6.
436
442
448
452
460
463
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Chapter 13
Magnetic Forces, Materials and Inductance
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The Transmission-Line Equations
Transmission-Line Parameters
Some Transmission-Line Examples
Graphical Methods
Several Practical Problems
Transients on Transmission Lines
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ix
x
CONTENTS
Chapter 14
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Waveguide and Antenna Fundamentals
484
14.1.
14.2.
14.3.
14.4.
14.5.
14.6.
485
488
497
501
506
514
Basic Waveguide Operation
Plane Wave Analysis of the Parallel-Plate Waveguide
Parallel-Plate Guide Analysis Using the Wave Equation
Rectangular Waveguides
Dielectric Waveguides
Basic Antenna Principles
Vector Analysis
Units
Material Constants
Origins of the Complex Permittivity
Answers to Selected Problems
529
Index
551
534
540
544
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