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ELECTROMAGNETICS FOR ENGINEERS Fawwaz T. Ulaby The University ofMichigan • Upper Saddle River, NJ 07458 LibraryofCongressCataloging-in-PublicationDataonfile. VicePresidentandEditorialDirector,ECS: MarciaJ. Horton Publisher: Tom Robbins VicePresidentandDirectorofProductionand Manufacturing,ESM: DavidW Riccardi ExecutiveManagingEditor: Vince O'Brien ManagingEditor: DavidA. George ProductionEditor: Craig Lillie DirectorofCreativeServices: PaulBelfanti CreativeDirector: Jayne Conte Designer: Bruce Kenselaar CoverPhoto: DaveShultz ArtEditor: GregDulles ManufacturingManager: Trudy Pisciotti ManufacturingBuyer: LisaMcDowell MarketingManager:Holly Stark • © 2005 byPearsonEducation,Inc. PearsonPrenticeHall PearsonEducation,Inc. • UpperSaddleRiver,NJ07458 Allrightsreserved.Nopartofthisbookmay bereproducedinany formatorbyany means,withoutpermissionin writingfrom thepublisher. PearsonPrenticeHal1® isatrademarkofPearsonEducation,Inc. Companyand productnames mentionedhereinarethetrademarksorregisteredtrademarksoftheirrespectiveowners. Theauthorandpublisherofthisbookhaveused theirbesteffortsinpreparingtillsbook.Theseeffortsincludethedevelopment, research, and testingofthetheoriesandprogramstodeterminetheireffectiveness.Theauthorandpublishermakenowarrantyofany kind,expressedor implied,withregardtotheseprogramsorthedocumentationcontainedinthisbook.Theauthorandpublishershallnotbeliableinanyeventfor incidentalorconsequentialdamagesinconnectionwith,orarisingoutof, thefurnishing, performance,oruseoftheseprograms. Printedin theUnitedStatesofAmerica 10 9 8 7 6 5 4 3 2 ISBN 0-13-149724-3 PearsonEducationLtd.,London PearsonEducation AustraliaPty.,Sydney PearsonEducationSingapore,Pte.Ltd. PearsonEducationNorthAsiaLtd.,HongKong PearsonEducationCanada,Inc., Toronto PearsonEducaci6ndeMexico, S.A.dec.Y. PearsonEducation-Japan, Tokyo PearsonEducationMalaysia,Pte.Ltd. PearsonEducationInc., UpperSaddleRiver; NewJersey For educating me, I dedicate this book to: The American University ofBeirut, and The University ofTexas For embracing me as one oftheir own, lowe gratitude to: The University ofKansas, and The University ofMichigan Timelines and Technology Briefs Timeline for Electromagnetics in the Classical Era 6 Timeline for Telecommunications 8 Timeline for Computer Technology 10 Global Positioning System 42 X-Ray Computed Tomography §6 Resistive Sensors 90 Capacitive Sensors 102 Noncontact Sensors 108 Electromagnets and Magnetic Relays 142 Magnetic Recording 150 Inductive Sensors 154 EMF Sensors 186 Liquid Crystal Display (LCD) 222 Microwave Ovens 272 Lasers 334 Bar-Code Readers 339 Radar Sensors 368 Communication Satellite 372 VI Contents Preface XIII 1 Introduction 2 1-1 Historical Timeline 3 1-1.1 EM In the ClassicalEra 3 1-1.2 EM in the Modern Era 4 1-2 Dimensions, Units, and Notation 5 1-3 The NatureofEM 12 1-3.1 The GravitationalForce: AUseful Analogue 12 1-3.2 Electric Fields 13 1-3.3 MagneticFields 15 1-3.4 Static and Dynamic Fields 17 1-4 TheElectromagneticSpectrum 18 2 Vector Algebra 22 2-1 Basic Laws ofVector Algebra 23 2-1.1 Equality ofTwo Vectors 24 2-1.2 Vector Addition and Subtraction 25 2-1.3 Position and Distance Vectors 25 2-1.4 VectorMultiplication 26 2-1.5 Scalarand VectorTripleProducts 29 2-2 Orthogonal Coordinate Systems 30 2-2.1 Cartesian Coordinates 31 2-2.2 Cylindrical Coordinates 31 2-2.3 Spherical Coordinates 35 2-3 Transformations between CoordinateSystems 37 2-3.1 Cartesian to CylindricalTransformations 37 Vll viii Contents 2-3.2 Cartesian to SphericalTransformations 39 2-3.3 Cylindrical to SphericalTransformations 41 2-3.4 Distance betweenTwoPoints 41 Problems 44 3 Vector Calculus 48 3-1 Gradientofa ScalarField 49 3-1.1 Gradient OperatorinCylindrical and SphericalCoordinates 51 3-1.2 Properties ofthe GradientOperator 51 3-2 Divergence ofaVectorField 53 3-2.1 DivergenceTheorem 55 3-3 Curl ofaVectorField 58 3-3.1 Vector Identities InvolvingtheCurl 60 3-3.2 Stokes's Theorem 60 3-4 LaplacianOperator 61 Problems 63 4 Electrostatics 66 4-1 Maxwell's Equations 67 4-2 Charge andCurrentDistributions 68 4-2.1 ChargeDensities 68 4-2.2 CurrentDensity 70 4-3 Coulomb's Law 71 4-3.1 ElectricFielddue to MultiplePointCharges 72 4-3.2 ElectricField due to aChargeDistribution 73 4-4 Gauss's Law 76 4-5 Electric ScalarPotential 79 4-5.1 Electric Potential as aFunction ofElectricField 79 4-5.2 Electric Potential due to PointCharges 81 4-5.3 Electric Potential due toContinuous Distributions 81 4-5.4 Electric Field as aFunctionofElectric Potential 82 4-5.5 Poisson'sEquation 83 4-6 Electrical Properties ofMaterials 84 4-7 Conductors 85 4-7.1 Resistance 87 4-7.2 Joule's Law 88 4-8 Dielectrics 89 Contents IX 4-9 Electric Boundary Conditions 94 4-9.1 Dielectric-ConductorBoundary 97 4-9.2 Conductor-<::onductorBoundary 98 4-10 Capacitance 99 4-11 Electrostatic Potential Energy 104 4-12 ImageMethod 105 Problems 110 5 Magnetostatics 118 5-1 Magnetic Forces and Torques 119 5-1.1 Magnetic Force on aCurrent-Carrying Conductor 121 5-1.2 Magnetic Torque on aCurrent-CarryingLoop 124 5-2 TheBiot-SavartLaw 127 5-2.1 Magnetic Field due to Surfaceand VolumeCurrentDistributions 128 5-2.2 Magnetic Field ofaMagnetic Dipole 131 5-3 Magnetic Forcebetween TwoParallel Conductors 132. 5-4 Maxwell's Magnetostatic Equations 133 5-4.1 Gauss's Law for Magnetism 134 5-4.2 Ampere's Law 134 5-5 VectorMagnetic Potential 139 5-6 Magnetic Properties ofMaterials 140 5-6.1 Orbital and Spin MagneticMoments 141 5-6.2 Magnetic Permeability 144 5-6.3 Magnetic Hysteresis ofFerromagnetic Materials 145 5-7 Magnetic Boundary Conditions 147 5-8 Inductance 149 5-8.1 Magnetic Fieldin a Solenoid 149 5-8.2 Self-inductance 152 5-8.3 Mutual Inductance 156 5-9 MagneticEnergy 157 Problems 159 6 Maxwell's Equations for Time-Varying Fields 168 6-1 Faraday's Law 169 6-2 Stationary Loop in aTime-Varying Magnetic Field 171 6-3 The Ideal Transformer 175 6-4 MovingConductorin a StaticMagnetic Field 176 6-5 TheElectromagnetic Generator 180 x Contents 6-6 Moving Conductorin aTime-Varying MagneticField 182 6-7 DisplacementCurrent 182 6-8 Boundary Conditions for Electromagnetics 185 6-9 Charge-CurrentContinuity Relation 188 6-10 Electromagnetic Potentials 189 Problems 190 7 Plane-Wave Propagation 196 7-1 Review ofWaves and Phasors 197 7-1.1 SinusoidalWavein aLossless Medium 198 7-1.2 SinusoidalWavein aLossy Medium 201 7-1.3 Review ofComplex Numbers 203 7-1.4 Review ofPhasors 205 7-2 Time-HarmonicFields 209 7-2.1 ComplexPermittivity 210 7-2.2 Wave Equations for a Charge-Free Medium 210 7-3 Plane-Wave PropagationinLossless Media 211 7-3.1 Uniform PlaneWaves 211 7-3.2 General Relation betweenE andH 215 7-4 Wave Polarization 216 7-4.1 Linear Polarization 217 7-4.2 CircularPolarization 218 7-4.3 EllipticalPolarization 220 7-5 Plane-Wave PropagationinLossy Media 225 7-5.1 Low-Loss Dielectric 227 7-5.2 GoodConductor 227 7-6 CurrentFlow in aGoodConductor 229 7-7 Electromagnetic PowerDensity 232 7-7.1 PlaneWave in aLossless Medium 233 7-7.2 PlaneWavein aLossyMedium 234 7-7.3 DecibelScalefor PowerRatios 235 Problems 237 8 Transmission Lines 244 8-1 General Considerations 245 8-1.1 The Role ofWavelength 245 8-1.2 PropagationModes 247 Contents xi 8-2 Lumped-ElementModel 248 8-3 Transmission-LineEquations 253 8-4 Wave Propagation on aTransmissionLine 254 8-5 The Lossless TransmissionLine 257 8-5.1 VoltageReflection Coefficient 258 8-5.2 StandingWaves 261 8-6 InputImpedance ofthe Lossless Line 265 8-7 Special Cases ofthe Lossless Line 268 8-7.1 Short-CircuitedLine 268 8-7.2 Open-CircuitedLine 270 8-7.3 Application ofShort-Circuit and Open-CircuitMeasurements 270 8-7.4 Lines ofLengthl = nA/2 274 8-7.5 Quarter-WaveTransformer 274 8-7.6 MatchedTransmission Line: ZL = Zo 274 8-8 PowerFlow on aLossless TransmissionLine 276 8-9 The Smith Chart 277 8-9.1 Parametric Equations 277 8-9.2 InputImpedance 282 8-9.3 SWR, Voltage Maximaand Minima 284 8-9.4 Impedanceto AdmittanceTransformations 285 8-10 Impedance Matching 291 8-11 Transients on TransmissionLines 295 8-11.1 TransientResponse 295 8-11.2 BounceDiagrams 299 Problems 302 9 Wave Reflection and Transmission 310 9-1 Wave Reflection and Transmission atNormal Incidence 312 9-1.1 BoundarybetweenLossless Media 312 9-1.2 Transmission-LineAnalogue 315 9-1.3 PowerFlow in Lossless Media 316 9-1.4 Boundary betweenLossy Media 319 9-2 Snell's Laws 321 9-3 FiberOptics 324