
▲
▲
Engineering Electromagnetics

eText Main Menu

Textbook Table of Contents

McGrawHill 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

▲
▲
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

eText Main Menu

Textbook Table of Contents

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

▲
▲
Boston

eText Main Menu

Textbook Table of Contents

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
TimeVarying 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

▲
▲
v

eText Main Menu

Textbook Table of Contents

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 easytoread 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 heavilymarked 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 coauthor, 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 endofchapter 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

▲
▲
xi

eText Main Menu

Textbook Table of Contents

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 problemsolving skills. I have also
moved the work more in the direction of communicationsoriented 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 lowerfrequency 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 asneeded 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 endofchapter problems are provided to
facilitate this. Answers to the drill problems are given below each problem.
Answers to selected endofchapter 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 onesemester 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 muchneeded 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 ElIbiary, 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 AlRizzo, Sultan

▲
▲
xii

eText Main Menu

Textbook Table of Contents

PREFACE
Qaboos University, Juri Silmberg, Ryerson Polytechnic University and Robert
M. Weikle II, University of Virginia. My editors at McGrawHill, 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 parttime husband and father for
many a weekend.

▲
▲
John A. Buck
Atlanta, 2000

eText Main Menu

Textbook Table of Contents

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

▲
▲
vii

eText Main Menu

Textbook Table of Contents

CONTENTS
Chapter 5
Chapter 6
Chapter 7
Chapter 8

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 TwoWire 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
▲
▲
viii
BiotSavart Law
Ampere's Circuital Law
Curl
Stokes' Theorem
Magnetic Flux and Magnetic Flux Density
The Scalar and Vector Magnetic Potentials
Derivation of the SteadyMagneticField Laws

eText Main Menu

Textbook Table of Contents

CONTENTS
Chapter 9
Chapter 10
Chapter 11
Chapter 12

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
TimeVarying 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
▲
▲
Chapter 13
Magnetic Forces, Materials and Inductance

The TransmissionLine Equations
TransmissionLine Parameters
Some TransmissionLine Examples
Graphical Methods
Several Practical Problems
Transients on Transmission Lines
eText Main Menu

Textbook Table of Contents

ix
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 ParallelPlate Waveguide
ParallelPlate 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
To find Appendix E, please visit the expanded website:
www.mhhe.com/engcs/electrical/haytbuck

▲
▲
x

eText Main Menu

Textbook Table of Contents

CHAPTER
1
VECTOR
ANALYSIS
Vector analysis is a mathematical subject which is much better taught by mathematicians than by engineers. Most junior and senior engineering students, however, have not had the time (or perhaps the inclination) to take a course in vector
analysis, although it is likely that many elementary vector concepts and operations were introduced in the calculus sequence. These fundamental concepts and
operations are covered in this chapter, and the time devoted to them now should
depend on past exposure.
The viewpoint here is also that of the engineer or physicist and not that of
the mathematician in that proofs are indicated rather than rigorously expounded
and the physical interpretation is stressed. It is easier for engineers to take a more
rigorous and complete course in the mathematics department after they have
been presented with a few physical pictures and applications.
It is possible to study electricity and magnetism without the use of vector
analysis, and some engineering students may have done so in a previous electrical
engineering or basic physics course. Carrying this elementary work a bit further,
however, soon leads to linefilling equations often composed of terms which all
look about the same. A quick glance at one of these long equations discloses little
of the physical nature of the equation and may even lead to slighting an old
friend.
Vector analysis is a mathematical shorthand. It has some new symbols,
some new rules, and a pitfall here and there like most new fields, and it demands
concentration, attention, and practice. The drill problems, first met at the end of
Sec. 1.4, should be considered an integral part of the text and should all be

▲
▲
1

eText Main Menu

Textbook Table of Contents

ENGINEERING ELECTROMAGNETICS
worked. They should not prove to be difficult if the material in the accompanying section of the text has been thoroughly understood. It take a little longer to
``read'' the chapter this way, but the investment in time will produce a surprising
interest.
1.1 SCALARS AND VECTORS
The term scalar refers to a quantity whose value may be represented by a single
(positive or negative) real number. The x; y, and z we used in basic algebra are
scalars, and the quantities they represent are scalars. If we speak of a body falling
a distance L in a time t, or the temperature T at any point in a bowl of soup
whose coordinates are x; y, and z, then L; t; T; x; y, and z are all scalars. Other
scalar quantities are mass, density, pressure (but not force), volume, and volume
resistivity. Voltage is also a scalar quantity, although the complex representation
of a sinusoidal voltage, an artificial procedure, produces a complex scalar, or
phasor, which requires two real numbers for its representation, such as amplitude
and phase angle, or real part and imaginary part.
A vector quantity has both a magnitude1 and a direction in space. We shall
be concerned with two and threedimensional spaces only, but vectors may be
defined in ndimensional space in more advanced applications. Force, velocity,
acceleration, and a straight line from the positive to the negative terminal of a
storage battery are examples of vectors. Each quantity is characterized by both a
magnitude and a direction.
We shall be mostly concerned with scalar and vector fields. A field (scalar
or vector) may be defined mathematically as some function of that vector which
connects an arbitrary origin to a general point in space. We usually find it
possible to associate some physical effect with a field, such as the force on a
compass needle in the earth's magnetic field, or the movement of smoke particles
in the field defined by the vector velocity of air in some region of space. Note that
the field concept invariably is related to a region. Some quantity is defined at
every point in a region. Both scalar fields and vector fields exist. The temperature
throughout the bowl of soup and the density at any point in the earth are
examples of scalar fields. The gravitational and magnetic fields of the earth,
the voltage gradient in a cable, and the temperature gradient in a solderingiron tip are examples of vector fields. The value of a field varies in general
with both position and time.
In this book, as in most others using vector notation, vectors will be indicated by boldface type, for example, A. Scalars are printed in italic type, for
example, A. When writing longhand or using a typewriter, it is customary to
draw a line or an arrow over a vector quantity to show its vector character.
(CAUTION: This is the first pitfall. Sloppy notation, such as the omission of the
line or arrow symbol for a vector, is the major cause of errors in vector analysis.)
1
We adopt the convention that ``magnitude'' infers ``absolute value''; the magnitude of any quantity is
therefore always positive.

▲
▲
2
...
Purchase answer to see full
attachment