Engineering electromagnetics william hayt and john buck 6th edition

| ▲ ▲ Engineering Electromagnetics | e-Text Main Menu | Textbook Table of Contents | 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 | ▲ ▲ 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 | www.elsolucionario.org e-Text 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 | www.elsolucionario.org e-Text Main Menu | Textbook Table of Contents | BRIEF CONTENTS Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter 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 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 à 551 à To find Appendix E, please visit the expanded book website: www.mhhe.com/engcs/electrical/haytbuck | ▲ ▲ v | www.elsolucionario.org e-Text 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 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 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 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 | ▲ ▲ xi | www.elsolucionario.org e-Text 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 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 and 7, as well as the later sections of Chapter 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 | ▲ ▲ xii | www.elsolucionario.org e-Text 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 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 | ▲ ▲ John A Buck Atlanta, 2000 | www.elsolucionario.org e-Text Main Menu | Textbook Table of Contents | xiii CONTENTS Chapter Chapter Chapter Chapter Preface xi Vector Analysis 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 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 | www.elsolucionario.org e-Text Main Menu | Textbook Table of Contents | CONTENTS Chapter Chapter Chapter Chapter | 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 ▲ ▲ viii 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 | www.elsolucionario.org e-Text Main Menu | Textbook Table of Contents | CONTENTS Chapter 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 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 ▲ ▲ Chapter 13 Magnetic Forces, Materials and Inductance | The Transmission-Line Equations Transmission-Line Parameters Some Transmission-Line Examples Graphical Methods Several Practical Problems Transients on Transmission Lines www.elsolucionario.org e-Text Main Menu | Textbook Table of Contents | ix l ‡ j2 sin l 2 cos l ‡ j3 sin l …41† Equations (40) and (41) are general results that enable us to calculate the net reflected wave amplitude and phase from two parallel interfaces between lossless media.1 Note the dependence on the interface spacing, l, and on the wavelength as measured in region 2, characterized by Of immediate importance to us is the fraction of the incident power that reflects from the dual interface and backpropagates in region As we found earlier, this fraction will be jÀj2 Also of interest is the transmitted power, which propagates away from the second interface in region It is simply the remaining power fraction, which is À jÀj2 The power in region stays constant in steady state; power leaves that region to form the reflected and transmitted waves, but is immediately replenished by the incident wave An important result of situations involving two interfaces is that it is possible to achieve total transmission in certain cases From (40), we see that total transmission occurs when À ˆ 0, or when in ˆ 1 In this case we say that the input impedance is matched to that of the incident medium There are a few methods of accomplishing this As a start, suppose that 3 ˆ 1 , and region is of thickness such that l ˆ m, where m is an integer Now ˆ 2=2 , where 2 is the wavelength as measured in region Therefore 2 l ˆ m 2 | ▲ ▲ For convenience, (38) and (39) have been written for a specific time at which the incident wave amplitude, ‡ Ex10 , occurs at z ˆ Àl This establishes a zero-phase reference at the front interface for the incident wave, and so it is from this reference that the reflected wave phase is determined Equivalently, we have repositioned the z ˆ point at the front interface Eq (41) allows this, since it is only a function of the interface spacing, l | www.elsolucionario.org e-Text Main Menu | Textbook Table of Contents | 403 ENGINEERING ELECTROMAGNETICS or lˆm 2 …42† With l ˆ m, the second region thickness is an integer multiple of half-wavelengths as measured in that medium Equation (41) now reduces to in ˆ 3 Thus the general effect of a multiple half-wave thickness is to render the second region immaterial to the results on reflection and transmission Equivalently, we have a single interface problem involving 1 and 3 Now, with 3 ˆ 1 , we have a matched input impedance, and there is no net reflected wave This method of choosing the region thickness is known as half-wave matching Its applications include, for example, antenna housings on airplanes known as radomes, which form a part of the fuselage The antenna, inside the aircraft, can transmit and receive through this layer which can be shaped to enable good aerodynamic characteristics Note that the half-wave matching condition no longer applies as we deviate from the wavelength that satisfies it When this is done, the device reflectivity increases (with increased wavelength deviation), so it ultimately acts as a bandpass filter Another application, typically seen in optics, is the Fabry-Perot interferometer This, in its simplest form, consists of a single block of glass or other transparent material, whose thickness, l, is set to transmit wavelengths which satisfy the condition, 2 ˆ 2l=m Often, it is desired to transmit only one wavelength, not several, as (42) would allow We would therefore like to ensure that adjacent wavelengths that are passed through the device are separated as far as possible This separation is in general given by mÀ1 À m ˆ Áf ˆ 2l 2l 2l : 2l À ˆ ˆ m À m m…m À 1† m2 Note that m is the number of half-wavelengths in region 2, or m ˆ 2l=2 , where 2 is the desired wavelength for transmission Thus : 2 …43† Áf ˆ 2l Áf is known as the free spectral range of the Fabry-Perot interferometer The interferometer can be used as a narrow-band filter (transmitting a desired wavelength and a narrow spectrum around this wavelength) if the spectrum to be filtered is narrower than the free spectral range h Example 12.4 Suppose we wish to filter an optical spectrum of full-width Ás ˆ 50 nm, and whose center wavelength is in the red part of the visible spectrum at 600 nm, where one nm (nanometer) is 10À9 m A Fabry-Perot filter is to be used, consisting of a lossless glass | ▲ ▲ 404 | www.elsolucionario.org e-Text Main Menu | Textbook Table of Contents | PLANE WAVES AT BOUNDARIES AND IN DISPERSIVE MEDIA plate in air, having relative permittivity HR ˆ R ˆ 2:1 We need to find the required range of glass thicknesses such that multiple wavelength orders will not be transmitted Solution We require that the free spectral range be greater than the optical spectral width, or Áf > Ás Thus, using (43) l< 22 2Ás where 600 2 ˆ p ˆ 414 nm 2:1 So l< 4142 ˆ 1:7  103 nm ˆ 1:7 m 2…50† where 1m (micrometer) = 10À6 m Fabricating a glass plate of this thickness or less is somewhat ridiculous to contemplate Instead, what is often used is an air space of thickness on this order, between two thick plates whose surfaces on the sides opposite the air space are antireflection coated This is in fact a more versatile configuration since the wavelength to be transmitted (and the free spectral range) can be adjusted by varying the plate separation Next we remove the restriction 1 ˆ 3 and look for a way to produce zero reflection Suppose we set l ˆ …2m À 1†=2, or an odd multiple of =2 This means that 2  l ˆ …2m À 1† 2 …m ˆ 1; 2; 3; F F F† or l ˆ …2m À 1† 2 …44† The thickness is an odd multiple of a quarter wavelength as measured in region Under this condition (41) reduces to in ˆ 22 3 …45† Typically, we choose the second region impedance to allow matching between given impedances 1 and 3 To achieve total transmission, we require that in ˆ 1 , so that the required second region impedance becomes | ▲ ▲ 2 ˆ | p 1 3 www.elsolucionario.org e-Text Main Menu | Textbook Table of Contents …46† | 405 ENGINEERING ELECTROMAGNETICS With the conditions given by (44) and (46) satisfied, we have performed quarterwave matching The design of anti reflective coatings for optical devices is based on this principle h Example 12.5 We wish to coat a glass surface with an appropriate dielectric layer to provide total transmission from air to the glass at a wavelength of 570 nm The glass has dielectric constant, R ˆ 2:1 Determine the required dielectric constant for the coating and its minimum thickness p Solution The known impedances are 1 ˆ 377  and 3 ˆ 377= 2:1 ˆ 260  Using (46) we have p 2 ˆ …377†…260† ˆ 313  The dielectric constant of region will then be  2 377 ˆ 1:45 R2 ˆ 313 The wavelength in region will be 570 2 ˆ p ˆ 473 nm 1:45 The minimum thickness of the dielectric layer is then lˆ 2 ˆ 118 nm ˆ 0:118 m The procedure in this section for evaluating wave reflection has involved calculating an effective impedance at the first interface, in , which is expressed in terms of the impedances that lie beyond the front surface This process of impedance transformation is more apparent when we consider problems involving more than two interfaces For example, consider the three-interface situation shown in Fig 12.7, where a wave is incident from the left in region We wish to determine the fraction of the incident power that is reflected and back-propagates in region 1, and the fraction of the incident power that is transmitted into region To this, we need to find the input impedance at the front surface (the interface between regions and 2) We start by transforming the impedance of region to form the input impedance at the boundary between regions and This is shown as in;b in the figure Using (41), we have in;b ˆ 3 | ▲ ▲ 406 | 4 cos lb ‡ j3 sin lb 3 cos lb ‡ j4 sin ... 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... | 23 ENGINEERING ELECTROMAGNETICS Thomas, G B., Jr., and R L Finney: ``Calculus and Analytic Geometry,'' 6th ed., Addison-Wesley Publishing Company, Reading, Mass., 1984 Vector algebra and the... 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