elementsofelectromagnetics sadiku 3rded 101208020917 phpapp01

www.elsolucionario.net DUPL PHYSICAL CONSTANTS Best Experimental Value Approximate Value for Problem Work Quantity (Units) Symbol Permittivity of free space (F/m) eu 8.854 x 10 Permeability of free space (H/m) /j,o 4i7 x 10" 12.6 x 10" Intrinsic impedance of free space (fl) rj o 376.6 120ir Speed of light in vacuum (m/s) c 2.998 x 108 X 108 Electron charge (C) e Electron mass (Kg) 12 -1.6030 x 10" l -1.6 x 10" mQ 9.1066 x 10" 31 9.1 x 10" 31 Proton mass (kg) mp 1.67248 x 10" 27 1.67 x 10" 27 Neutron mass (Kg) ma 1.6749 x 10" 27 1.67 x 10 Boltzmann constant (J/K) K 1.38047 x 10" 23 1.38 x 10" 23 Avogadro's number (/Kg-mole) N 6.0228 x 1026 x 1026 Planck's constant (J • s) h 6.624 x 10" 34 6.62 x 10" Acceleration due to gravity (m/s2) g 9.81 9.8 Universal contant of gravitation (m2/Kg • s2) G 6.658 x - " 6.66 x 10" 11 Electron-volt (J) eV 1.6030 x 10" 19 1.6 x 10" 27 www.elsolucionario.net CONTENTS Preface xiii A Note to the Student xvi PART : VECTOR ANALYSIS Vector Algebra 1.1 11.2 1.3 1.4 115 1.6 1.7 1.8 Introduction A Preview of the Book Scalars and Vectors Unit Vector Vector Addition and Subtraction Position and Distance Vectors Vector Multiplication 11 Components of a Vector 16 Summary 22 Review Questions 23 Problems 25 Coordinate Systems and Transformation 2.1 2.2 2.3 2.4 f2.5 28 Introduction 28 Cartesian Coordinates (x, y, z) 29 Circular Cylindrical Coordinates (p, , z)29 Spherical Coordinates (r, d, z) 32 Constant-Coordinate Surfaces 41 Summary 46 Review Questions 47 Problems 49 VII www.elsolucionario.net Contents Vector Calculus 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 t3.9 53 Introduction 53 Differential Length, Area, and Volume 53 Line, Surface, and Volume Integrals 60 Del Operator 63 Gradient of a Scalar 65 Divergence of a Vector and Divergence Theorem Curl of a Vector and Stokes's Theorem 75 Laplacian of a Scalar 83 Classification of Vector Fields 86 Summary 89 Review Questions 90 Problems 93 69 PART : ELECTROSTATICS Electrostatic Fields 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 103 Introduction 103 Coulomb's Law and Field Intensity 104 Electric Fields due to Continuous Charge Distributions 111 Electric Flux Density 122 Gauss's Law—Maxwell's Equation 124 Applications of Gauss's Law 126 Electric Potential 133 Relationship between E and V—Maxwell's Equation 139 An Electric Dipole and Flux Lines 142 Energy Density in Electrostatic Fields 146 Summary 150 Review Questions 153 Problems 155 Electric Fields in Material Space 5.1 5.2 5.3 5.4 5.5 5.6 f 5.7 5.8 161 Introduction 161 Properties of Materials 161 Convection and Conduction Currents 162 Conductors 165 Polarization in Dielectrics 171 Dielectric Constant and Strength 774 Linear, Isotropic, and Homogeneous Dielectrics 175 Continuity Equation and Relaxation Time 180 www.elsolucionario.net CONTENTS 5.9 Boundary Conditions 182 Summary 191 Review Questions 192 Problems 194 Electrostatic Boundary-Value Problems 6.1 6.2 f 6.3 6.4 6.5 6.6 199 Introduction 199 Poisson's and Laplace's Equations 199 Uniqueness Theorem 201 General Procedure for Solving Poisson's or Laplace's Equation 202 Resistance and Capacitance 223 Method of Images 240 Summary 246 Review Questions 247 Problems 249 PART 3: MAGNETOSTATICS Magnetostatic Fields 7.1 7.2 7.3 7.4 7.5 7.6 7.7 f 7.8 261 Introduction 261 Biot-Savart's Law 263 Ampere's Circuit Law—Maxwell's Equation 273 Applications of Ampere's Law 274 Magnetic Flux Density—Maxwell's Equation 281 Maxwell's Equations for Static EM Fields 283 Magnetic Scalar and Vector Potentials 284 Derivation of Biot-Savart's Law and Ampere's Law Summary 292 Review Questions 293 Problems 296 Magnetic Forces, Materials, and Devices 8.1 8.2 8.3 8.4 8.5 f 8.6 8.7 8.8 304 Introduction 304 Forces due to Magnetic Fields 304 Magnetic Torque and Moment 316 A Magnetic Dipole 318 Magnetization in Materials 323 Classification of Magnetic Materials 327 Magnetic Boundary Conditions 330 Inductors and Inductances 336 290 IX www.elsolucionario.net Contents 8.9 f8.10 18.11 Magnetic Energy Magnetic Circuits Force on Magnetic Summary 354 Review Questions Problems 358 339 347 Materials 349 356 PART 4: WAVES AND APPLICATIONS Maxwell's Equations 369 9.1 9.2 9.3 9.4 9.5 t9.6 9.7 10 Electromagnetic Wave Propagation 10.1 tl0.2 10.3 10.4 10.5 10.6 10.7 10.8 f 10.9 11 Introduction 369 Faraday's Law 370 Transformer and Motional EMFs 372 Displacement Current 381 Maxwell's Equations in Final Forms 384 Time-Varying Potentials 387 Time-Harmonic Fields 389 Summary 400 Review Questions 407 Problems 404 Introduction 410 Waves in General 411 Wave Propagation in Lossy Dielectrics 417 Plane Waves in Lossless Dielectrics 423 Plane Waves in Free Space 423 Plane Waves in Good Conductors 425 Power and the Poynting Vector 435 Reflection of a Plane Wave at Normal Incidence Reflection of a Plane Wave at Oblique Incidence Summary 462 Review Questions 464 Problems 466 Transmission Lines 11.1 11.2 11.3 11.4 11.5 410 473 Introduction 473 Transmission Line Parameters 474 Transmission Line Equations 477 Input Impedance, SWR, and Power 484 The Smith Chart 492 440 451 www.elsolucionario.net CONTENTS 11.6 f 11.7 111.8 Some Applications of Transmission Lines Transients on Transmission Lines 512 Microstrip Transmission Lines 524 Summary 528 Review Questions 530 Problems 533 12 Waveguides 12.1 12.2 12.3 12A 12.5 12.6 tl2.7 12.8 13 Antennas 13.1 13.2 13.3 13.4 13.5 13.6 13.7 113.8 tl3.9 14 542 Introduction 542 Rectangular Waveguides 543 Transverse Magnetic (TM) Modes 547 Transverse Electric (TE) Modes 552 Wave Propagation in the Guide 563 Power Transmission and Attenuation 565 Waveguide Current and Mode Excitation 569 Waveguide Resonators 575 Summary 581 Review Questions 582 Problems 583 588 Introduction 588 Hertzian Dipole 590 Half-Wave Dipole Antenna 594 Quarter-Wave Monopole Antenna 598 Small Loop Antenna 599 Antenna Characteristics 604 Antenna Arrays 612 Effective Area and the Friis Equation 62 / The Radar Equation 625 Summary 629 Review Questions 630 Problems 632 Modern Topics 14.1 14.2 14.3 14.4 505 638 Introduction 638 Microwaves 638 Electromagnetic Interference and Compatibility Optical Fiber 649 Summary 656 Review Questions 656 Problems 658 644 XI www.elsolucionario.net \ii • Contents 15 Numerical Methods 15.1 tl5.2 15.3 15.4 15.5 660 Introduction 660 Field Plotting 667 The Finite Difference Method 669 The Moment Method 683 The Finite Element Method 694 Summary 713 Review Questions 714 Problems / Appendix A Mathematical Formulas 727 Appendix B Material Constants 737 Appendix C Answers to Odd-Numbered Problems 740 Index 763 www.elsolucionario.net PREFACE The fundamental objectives of the book remains the same as in the first edition—to present electromagnetic (EM) concepts in a clearer and more interesting manner than earlier texts This objective is achieved in the following ways: To avoid complicating matters by covering EM and mathematical concepts simultaneously, vector analysis is covered at the beginning of the text and applied gradually This approach avoids breaking in repeatedly with more background on vector analysis, thereby creating discontinuity in the flow of thought It also separates mathematical theorems from physical concepts and makes it easier for the student to grasp the generality of those theorems Each chapter starts with a brief introduction that serves as a guide to the whole chapter and also links the chapter to the rest of the book The introduction helps students see the need for the chapter and how the chapter relates to the previous chapter Key points are emphasized to draw the reader's attention to them A brief summary of the major concepts is provided toward the end of the chapter To ensure that students clearly understand important points, key terms are defined and highlighted Essential formulas are boxed to help students identify them Each chapter includes a reasonable amount of examples with solutions Since the examples are part of the text, they are clearly explained without asking the reader to fill in missing steps Thoroughly worked-out examples give students confidence to solve problems themselves and to learn to apply concepts, which is an integral part of engineering education Each illustrative example is followed by a problem in the form of a Practice Exercise, with the answer provided At the end of each chapter are ten review questions in the form of multiple-choice objective items It has been found that open-ended questions, although intended to be thought provoking, are ignored by most students Objective review questions with answers immediately following them provide encouragement for students to the problems and gain immediate feedback A large number of problems are provided are presented in the same order as the material in the main text Problems of intermediate difficulty are identified by a single asterisk; the most difficult problems are marked with a double asterisk Enough problems are pro- XIII www.elsolucionario.net \iv • Preface vided to allow the instructor to choose some as examples and assign some as homework problems Answers to odd-numbered problems are provided in Appendix C Since most practical applications involve time-varying fields, six chapters are devoted to such fields However, static fields are given proper emphasis because they are special cases of dynamic fields Ignorance of electrostatics is no longer acceptable because there are large industries, such as copier and computer peripheral manufacturing, that rely on a clear understanding of electrostatics The last chapter covers numerical methods with practical applications and computer programs This chapter is of paramount importance because most practical problems are solvable only by using numerical techniques Over 130 illustrative examples and 400 figures are given in the text Some additional learning aids, such as basic mathematical formulas and identities, are included in the Appendix Another guide is a special note to students, which follows this preface In this edition, a new chapter on modern topics, such as microwaves, electromagnetic interference and compatibility, and fiber optics, has been added Also, the Fortran codes in previous editions have been converted to Matlab codes because it was felt that students are more familiar with Matlab than with Fortran Although this book is intended to be self-explanatory and useful for self-instruction the personal contact that is always needed in teaching is not forgotten The actual choice o1 course topics, as well as emphasis, depends on the preference of the individual instructor For example, the instructor who feels that too much space is devoted to vector analysis o: static fields may skip some of the materials; however, the students may use them as refer ence Also, having covered Chapters to 3, it is possible to explore Chapters to 15 In structors who disagree with the vector-calculus-first approach may proceed with Chapter; and 2, then skip to Chapter and refer to Chapter as needed Enough material i covered for two-semester courses If the text is to be covered in one semester, some sec tions may be skipped, explained briefly, or assigned as homework Sections marked wit! the dagger sign (t) may be in this category A suggested schedule for a four-hour semester coverage is on page xv Acknowledgments I would like to thank Peter Gordon and the editorial and production staff of Oxford Un versity Press for a job well done This edition has benefited from the insightful commeni of the following reviewers: Leo C Kempel, Michigan State University; Andrew Diene University of California, Davis; George W Hanson, University of Wisconsin-Milwaukei Samir El-Ghazaly, Arizona State University; and Sadasiva M Rao, Auburn University, am greatly indebted to Raymond Garcia, Jerry Sagliocca, and Dr Oladega Soriyan f< helping with the solutions manual and to Dr Saroj Biswas for helping with Matlab I a: grateful to Temple University for granting me a leave in Fall 1998, during which I was ab to work on the revision of this book I owe special thanks to Dr Keya Sadeghipour, de; of the College of Engineering, and Dr John Helferty, chairman of the Department of Ele trical and Computer Engineering for their constant support As always, particular than] www.elsolucionario.net APPENDIX C 0, / (p2-a2 2 2-KP \b - a I 7.17 (b) pb 7.19 (a) -2a, A/m (b) Proof, both sides equal -30 A 7.21 (a) 8Oa0nWb/m (b) 1.756/i Wb 7.23 (a) 31.433, A/m (b) 12.79ax + 6.3663, A/m 7.25 13.7 nWb 7.27 (a) magnetic field (b) magnetic field (c) magnetic field 7.29 (14a, + 42a0) X 104 A/m, -1.011 Wb 7.31 IoP a 2?ra2 * 7.33 — / 7.35 A/m 8/Xo/ 28x 7.37 (a) 50 A (b) -250 A 7.39 Proof CHAPTER 8.1 -4.4ax + 1.3a, + 11.4a, kV/m 8.3 (a) (2, 1.933, -3.156) (b) 1.177 J 8.5 (a) Proof 8.7 8.9 8.11 8.13 8.15 I -86.4azpN -15.59 mJ 1.949axmN/m 2.133a* - 0.2667ay Wb/m2 (a) -18.52azmWb/m2 (b) -4a,mWb/m2 (c) -Ilia, + 78.6a,,mWb/m2 pTMl3 TEM TE14,TM14 TE , TE , T M T E l , TM 0.8333 1.667 1.863 2.357 2.5 3.333 3.727 4.167 4.488 12.15 (a) 1.193 (b) 0.8381 12.17 4.917 4ir i\ b 12.21 0.04637 Np/m, 4.811 m 12.23 (a) 2.165 X 10~2Np/m (b) 4.818 X 10" Np/m 12.25 Proof r (mzx\ (niry\ piK — ) Ho sin cos cos 12.27 Proof, — j V a J \ b J c 12.29 (a) TEo,, (b) TM 110 (c) TE 101 12.31 See Table C.2 TABLE C.2 Mode Oil 110 101 102 120 022 fr (GHz) 1.9 3.535 3.333 3.8 4.472 3.8 12.33 (a) 6.629 GHz (b) 6,387 12.35 2.5 (-sin 30TTX COS 30X^3^ + cos 30irx sin 3070^) sin X 109 U 755 www.elsolucionario.net 756 M Appendix C CHAPTER 13 sin (w? - /3r)(-sin