Advanced Theoretical and Numerical Electromagnetics, Volume 2: Field representations and the Method of Moments

569 Pages·2022·17.486 MB·English

by  Vito Lancellotti

Advanced Theoretical and
Numerical Electromagnetics
TheACESSeriesonComputationalandNumericalModellinginElectrical
Engineering
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Advanced Theoretical and
Numerical Electromagnetics
Volume 2: Field representations
and the Method of Moments
Vito Lancellotti
TheInstitutionofEngineeringandTechnology
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Contents
Listoffigures xv
Listoftables xxv
Listofexamples xxvii
Abouttheauthor xxix
Foreword xxxi
Preface xxxiii
Acknowledgements xxxvii
1 Fundamentalnotionsandtheorems 1
1.1 Theelectromagneticfield 1
1.2 TheMaxwellequations 4
1.2.1 Integralorglobalform 4
1.2.2 Differentialorlocalorpointform 6
1.3 TheFaradaylawforslowlymovingconductors 14
1.4 Displacementcurrent 20
1.5 Time-harmonicfieldsandsources 23
1.6 Constitutiverelationships 26
1.7 Boundaryconditionsforfieldsandcurrents 30
1.8 Waveequations 41
1.8.1 Timedomain 43
1.8.2 Frequencydomain 46
1.9 Electromagneticradiation 48
1.10 Conservationofelectromagneticenergy 51
1.10.1 Poyntingtheoreminthetimedomain 51
1.10.2 Poyntingtheoreminthefrequencydomain 58
1.11 Conservationofelectromagneticmomentum 64
1.12 Conservationofelectromagneticangularmomentum 72
References 75
2 StaticelectricfieldsI 79
2.1 Lawsofelectrostatics 79
2.2 ScalarpotentialandthePoissonequation 83
2.3 Physicalmeaningofthescalarpotential 89
2.4 Boundaryconditionsforthescalarpotential 90
2.5 Uniquenessofthestaticsolutions 91
2.5.1 Scalarpotential 91
2.5.2 Electrostaticfield 102
2.6 Thethree-dimensionalstaticGreenfunction 105
2.6.1 Unboundedhomogeneousisotropicmedium 106
2.6.2 Unboundedhomogeneousanisotropicmedium 107
viii AdvancedTheoreticalandNumericalElectromagnetics
2.7 Integralrepresentationofthescalarpotential 109
2.8 Volumepotential 120
2.9 Double-layerpotential 131
2.10 Single-layerpotential 135
References 144
3 StaticelectricfieldsII 147
3.1 Scalarpotentialduetosurfacecharges 147
3.2 Integralrepresentationoftheelectrostaticfield 151
3.3 OtherGreenfunctionsforstaticproblems 154
3.3.1 TheDirichletGreenfunction 154
3.3.2 TheNeumannGreenfunction 158
3.4 PropertiesofthestaticGreenfunctions 159
3.5 Laplaceequationandboundaryvalueproblems 163
3.5.1 Polarsphericalcoordinates 163
3.5.2 Circularcylindricalcoordinates 175
3.6 Multipoleexpansionofthescalarpotential 182
3.6.1 TaylorseriesoftheGreenfunction 182
3.6.2 Sphericalharmonics 187
3.7 Polarizationvector 191
3.8 TheKelvinandEarnshawtheorems 197
3.9 Imageprincipleinelectrostatics 206
3.10 Singularelectricfields 211
References 215
4 StationarymagneticfieldsI 219
4.1 StationarylimitofMaxwell’sequations 219
4.2 VectorpotentialandthevectorPoissonequation 229
4.3 Boundaryconditionsforthevectorpotential 233
4.4 Magneticscalarpotential 236
4.5 Magneticdipoles 238
4.6 Energyandmomentuminthestationarylimit 242
4.7 Uniquenessofthestationarysolutions 242
4.7.1 Vectorpotential 242
4.7.2 Magneticentitiesinthepresenceofmagneticmedia 247
4.7.3 Magneticentitiesinthepresenceofconductors 252
References 260
5 StationarymagneticfieldsII 263
5.1 Integralrepresentations 263
5.1.1 Vectorpotentialinanisotropicmedium 263
5.1.2 Magneticinductionandmagneticfield 275
5.1.3 Vectorpotentialandmagneticentitiesinananisotropicmedium 279
5.2 Vectorpotentialduetosurfacecurrents 284
5.3 Physicalmeaningofthevectorpotential 289
5.4 Geometricalmeaningofthescalarpotential 293
5.5 Multipoleexpansionofthevectorpotential 296
5.6 Magnetizationvector 300
Contents ix
5.7 Magneticforcesbetweensteadycurrents 311
References 316
6 Propertiesofelectromagneticfields 319
6.1 Principleofsuperposition 319
6.2 Well-posednessoftheMaxwellequations 325
6.3 Uniquenessinthetimedomain 326
6.3.1 Boundedregions 327
6.3.2 Unboundedregions 331
6.4 Uniquenessinthefrequencydomain 337
6.4.1 Boundedregions 338
6.4.2 Unboundedregions 353
6.5 Magneticchargesandcurrents 359
6.6 Boundaryconditionswithmagneticsources 365
6.7 Dualitytransformations 368
6.8 Reciprocitytheorems 371
6.8.1 Frequencydomain 371
6.8.2 Non-reciprocalmedia 388
6.8.3 Timedomain 389
6.9 Othersymmetryrelationships 391
6.9.1 Electrostaticfields 391
6.9.2 Stationaryfieldsandsteadycurrents 398
References 402
7 Electromagneticwaves 407
7.1 Time-domainuniformplanewaves 407
7.2 Time-harmonicplanewaves 409
7.2.1 Losslessisotropicmedium 410
7.2.2 Lossyisotropicmedium 421
7.3 Polarizationofplanewaves 430
7.4 Plane-wavepropagationinlayeredisotropicmedia 433
7.4.1 Reflectionandtransmissionataplanarinterface 434
7.4.2 Networkequivalentofamulti-layeredmedium 445
7.5 Time-domainuniformcylindricalwaves 460
7.6 Thetwo-dimensionaltime-domainGreenfunction 470
7.7 Time-domaintransverseelectric-magneticsphericalwaves 479
7.8 Non-radiatingsources 485
References 490
8 Time-varyingelectromagneticfieldsI 493
8.1 TheHelmholtzdecomposition 493
8.1.1 Unboundedregions 493
8.1.2 Boundedregions 502
8.2 Electrodynamicpotentialsandgaugetransformations 513
8.3 Boundaryconditionsfortheelectrodynamicpotentials 519
8.4 Hertzianpotentials 523
8.5 ThescalarHelmholtzequation 527
8.5.1 Polarsphericalcoordinates 527