The classical theory of fields: electromagnetism
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Series: | Graduate texts in Physics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 446 S. graph. Darst. |
| ISBN: | 3642232043 9783642232046 |
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Record in the Search Index
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IMAGE 1
CONTENTS
1 ORIGINS AND CONCEPTS 1
1.1 INTRODUCTION 1
1.2 MAGNETISM 2
1.3 GRAVITATION 3
1.4 FARADAY, THOMSON, AND MAXWELL 3
1.5 GRAVITATION A VECTOR FIELD 4
1.6 CHARGES AND ELECTRIC FIELDS 5
1.7 PRIESTLY'S SPECULATION 6
1.8 VOLTAIC CELL 7
1.9 CURRENTS AND MAGNETIC FIELDS 8
1.9.1 OERSTED 8
1.9.2 AMPERE 10
1.9.3 ELECTRICAL CURRENT 11
1.10 INDUCED ELECTRIC FIELD 12
1.11 THE MATHEMATICAL THEORY 13
1.11.1 THE FIELD EQUATIONS 13
1.11.2 MAXWELL 15
1.12 EXPERIMENTAL EVIDENCE 20
1.12.1 WAVES IN THE LABORATORY 20
1.12.2 WAVE ENERGY AND MOMENTUM 23
1.13 MICHELSON AND MORLEY EXPERIMENT 24
1.14 RELATIVITY 27
1.15 SUMMARY 29
QUESTIONS 30
2 MATHEMATICAL BACKGROUND 33
2.1 INTRODUCTION 33
2.2 VECTORS 34
2.2.1 THE VECTOR SPACE 34
2.2.2 REPRESENTATION 36
2.2.3 SCALAR PRODUCT 39
2.2.4 VECTOR PRODUCT 40
VII
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1013511220
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
2.3 MULTIVARIATE FUNCTIONS 41
2.3.1 DIFFERENTIALS 42
2.3.2 CYLINDRICAL COORDINATES 43
2.3.3 SPHERICAL COORDINATES 44
2.4 ANALYTIC FUNCTIONS 45
2.4.1 TAYLORSERIES 45
2.4.2 ANALYTICITY 46
2.5 VECTOR CALCULUS 46
2.5.1 FIELD QUANTITIES 46
2.5.2 THEGRADIENT 47
2.5.3 THE DIVERGENCE 48
2.5.4 THE CURL 54
2.5.5 THE LAPLACIAN OPERATOR 61
2.6 DIFFERENTIAL EQUATIONS 62
2.6.1 HELMHOLTZ'THEOREM 64
2.6.2 THE DEL OPERATOR 65
2.6.3 DIRAC DELTA FUNCTION 66
2.7 SUMMARY 71
EXERCISES 72
ELECTROSTATICS 79
3.1 INTRODUCTION 79
3.2 COULOMB'SLAW 79
3.2.1 COULOMB'S EXPERIMENT 79
3.2.2 UNITS 81
3.3 SUPERPOSITION 81
3.4 DISTRIBUTIONS OF CHARGES 82
3.4.1 DISTRIBUTION OF POINT CHARGES 83
3.4.2 VOLUME CHARGE DENSITY 84
3.4.3 SURFACE CHARGE DENSITY 85
3.5 THE FIELD CONCEPT 87
3.6 DIVERGENCE AND CURL OF E 89
3.7 INTEGRAL ELECTROSTATIC FIELD EQUATIONS 91
3.7.1 GAUSS'THEOREM 92
3.7.2 STOKES' THEOREM 93
3.8 SUMMARY 93
EXERCISES 94
THE SCALAR POTENTIAL 99
4.1 INTRODUCTION 99
4.2 POTENTIAL ENERGY 99
4.3 POTENTIAL SURFACES 101
4.4 POISSON'S EQUATION 101
4.5 MULTIPOLE EXPANSION 108
4.6 ENERGY STORAGE 110
4.6.1 ELECTROSTATIC ENERGY DENSITY 110
4.6.2 ENERGY OF A SET OF CONDUCTORS I LL
IMAGE 3
CONTENTS IX
4.7 SUMMARY 116
EXERCISES 117
5 MAGNETOSTATICS 123
5.1 INTRODUCTION 123
5.2 CURRENT 124
5.2.1 CURRENT DENSITY 124
5.2.2 CHARGE CONSERVATION 125
5.3 OERSTED'S EXPERIMENT 126
5.4 AMPERE'S EXPERIMENT 129
5.4.1 DIRECTION OF THE FORCE 130
5.4.2 THE CONSTANT 131
5.5 CONSEQUENCES OF AMPERE'S EXPERIMENT 132
5.5.1 FORCE ON A CHARGE 132
5.5.2 FIELD FROM A STRAIGHT WIRE 133
5.5.3 BIOT-SAVART LAW 134
5.6 SUPERPOSITION 136
5.7 MULTIPOLE EXPANSION 138
5.8 DIVERGENCE AND CURL OF B 141
5.9 GAUGE TRANSFORMATION 142
5.10 THE STATIC FIELD EQUATIONS 143
5.11 SUMMARY 145
EXERCISES 145
6 APPLICATIONS OF MAGNETOSTATICS 149
6. 1 INTRODUCTION 149
6.2 BIOT-SAVART LAW 149
6.3 VECTOR POTENTIAL 151
6.4 SUMMARY 159
EXERCISES 159
7 PARTICLE MOTION 165
7.1 INTRODUCTION 165
7.2 ANALYTICAL MECHANICS 165
7.2.1 EULER-LAGRANGE FORMULATION 165
7.2.2 HAMILTONIAN FORMULATION 166
7.3 ELECTRODYNAMICS 167
7.3.1 THE LANGRANGIAN 167
7.3.2 THE HAMILTONIAN 169
7.4 PARTICLE MOTION 169
7.4.1 MAGNETIC FIELDS 169
7.4.2 ELECTRIC AND MAGNETIC FIELDS 176
7.5 PLASMAS 180
7.6 SUMMARY 182
EXERCISES 182
IMAGE 4
X CONTENTS
8 GREEN'S FUNCTIONS 187
8. 1 INTRODUCTION 187
8.2 GENERAL FORMULATION 188
8.3 POISSON'S EQUATION 189
8.4 GREEN'S FUNCTION IN ONE DIMENSION 190
8.5 VECTOR POTENTIAL 200
8.6 SUMMARY 200
EXERCISES 201
9 LAPLACE'S EQUATION 205
9.1 INTRODUCTION 205
9.2 FORMS OF LAPLACE'S EQUATION 206
9.3 RECTANGULAR COORDINATES 207
9.3.1 EIGENVALUE PROBLEMS 207
9.4 CYLINDRICAL COORDINATES 211
9.5 SPHERICAL COORDINATES 214
9.6 SUMMARY 219
10 TIME DEPENDENCE 221
10.1 INTRODUCTION 221
10.2 FARADAY'S LAW 221
10.3 DISPLACEMENT CURRENT 224
10.4 MAGNETOSTATIC ENERGY 226
10.5 MAXWELL'S EQUATIONS 228
10.6 SUMMARY 230
EXERCISES 230
11 ELECTROMAGNETIC WAVES 239
11.1 INTRODUCTION 239
11.2 WAVE EQUATIONS 240
11.3 PLANE WAVES 241
11.4 PLANE WAVE STRUCTURE 244
11.4.1 POLARIZATION 246
11.5 GENERAL WAVE SOLUTIONS 249
11.5.1 SPREADOFWAVES 249
11.5.2 REPRESENTATION IN PLANE WAVES 250
11.5.3 FOURIER TRANSFORM 250
11.6 FOURIER TRANSFORMED EQUATIONS 254
11.7 SCALAR AND VECTOR POTENTIALS 255
11.8 SUMMARY 256
EXERCISES 257
12 ENERGY AND MOMENTUM 261
12.1 INTRODUCTION 261
12.2 TRANSPORT THEOREM 262
12.3 ELECTROMAGNETIC FIELD ENERGY 263
12.4 ELECTROMAGNETIC FIELD MOMENTUM 266
IMAGE 5
CONTENTS XI
12.5 STATIC FIELD ENERGIES 269
12.6 SUMMARY 270
EXERCISES 270
13 SPECIAL RELATIVITY 273
13.1 INTRODUCTION 273
13.2 THE NEW KINEMATICS 274
13.2.1 TIME 275
13.2.2 SPACE 278
13.2.3 LORENTZ TRANSFORMATION 280
13.3 MINKOWSKI SPACE-TIME 280
13.3.1 FOUR DIMENSIONS 280
13.3.2 FOUR VECTORS 282
13.3.3 THE MINKOWSKI AXIOM 282
13.3.4 THELIGHTCONE 283
13.4 FORMAL LORENTZ TRANSFORM 284
13.5 TIME AND SPACE 285
13.5.1 TIMEDILATION 286
13.5.2 SPACE CONTRACTION 287
13.5.3 VELOCITIES 289
13.6 TENSORS 291
13.7 METRICSPACE 293
13.8 FOUR-VELOCITY 294
13.9 MASS, MOMENTUM, AND ENERGY 295
13.9.1 MASS 295
13.9.2 FOUR-MOMENTUM 296
13.9.3 ENERGY 297
13.10 ELECTRODYNAMICS 300
13.10.1 FIELD EQUATIONS 300
13.10.2 DERIVATIVES 300
13.10.3 CURRENT AND POTENTIAL VECTORS 302
13.10.4 ELECTRODYNAMIC COVARIANCE 303
13.10.5 FIELD STRENGTH TENSOR 304
13.11 MOVING CHARGES 306
13.12 SUMMARY 311
EXERCISES 312
14 RADIATION 317
14.1 INTRODUCTION 317
14.2 WAVES FROM SOURCES '317
14.3 LIENARD-WIECHERT POTENTIALS 322
14.4 PLANE WAVES 326
14.5 SOURCES 327
14.5.1 DIPOLE RADIATION 328
14.5.2 CHARGE IN A MAGNETIC FIELD 330
14.6 SUMMARY 331
EXERCISES 332
IMAGE 6
XII CONTENTS
15 FIELDS IN MATTER 335
15.1 INTRODUCTION 335
15.2 EXPERIMENTS 336
15.2.1 DIELECTRICS IN CAPACITORS 336
15.2.2 SOLID DIELECTRICS 337
15.2.3 MAGNETIC CORES IN INDUCTORS 339
15.2.4 MAGNETISM IN SOLIDS 340
15.3 POTENTIALS FROM SLOWLY VARYING FIELDS 342
15.3.1 ATOMS AND MULTIPOLE EXPANSIONS 342
15.3.2 POLARIZATION AND MAGNETIZATION DENSITIES 345 15.3.3 POLARIZATION
CHARGES AND MAGNETIZATION CURRENTS 347 15.4 INTERACTION OF FIELDS 349
15.5 MAXWELL'S EQUATIONS IN MATTER 350
15.6 CONSTITUTIVE EQUATIONS 351
15.6.1 POLARIZATION 351
15.6.2 MAGNETIZATION 351
15.6.3 PERMITTIVITY AND PERMEABILITY 352
15.7 BOUNDARY CONDITIONS ON FIELDS 352
15.7.1 ELECTRIC FIELD 353
15.7.2 MAGNETIC FIELD 355
15.8 FERROMAGNETISM 357
15.8.1 HYSTERESIS 360
15.8.2 MODERN DIRECTIONS 361
15.9 SUMMARY 361
EXERCISES 362
16 WAVES IN DISPERSIVE MEDIA 373
16.1 INTRODUCTION 373
16.2 WAVES IN MATTER 374
16.2.1 REPRESENTATION OF WAVES 374
16.2.2 DISPERSION RELATION IN MATTER 375
16.2.3 TRANSVERSE AND LONGITUDINAL WAVES 376
16.2.4 WAVE CONDUCTIVITY 377
16.2.5 WAVE ENERGY 377
16.3 NEARLY MONOCHROMATIC WAVES 378
16.3.1 DISPERSION OF MONOCHROMATIC WAVES 378
16.3.2 TIME AND SPACE AVERAGES 379
16.3.3 FIELD ENERGY 381
16.3.4 PARTICLE ENERGY 385
16.4 NOTE ON GROUP VELOCITY 387
16.5 APPLICATION 389
16.6 SUMMARY 391
EXERCISES 392
IMAGE 7
CONTENTS XIII
APPENDIX A VECTOR CALCULUS 393
A. 1 DIFFERENTIAL OPERATORS 393
A.2 DIFFERENTIAL OPERATOR IDENTITIES 394
APPENDIX B DIRAC DELTA SEQUENCES 395
APPENDIX C DIVERGENCE AND CURL OF B 397
APPENDIX D GREEN'S THEOREM 399
APPENDIX E LAPLACE'S EQUATION 401
APPENDIX F POISSON'S EQUATION 407
APPENDIX G HEIMHOLTE' EQUATION 409
APPENDIX H LEGENDRE'S EQUATION 413
APPENDIX I JACOBIANS 417
APPENDIX J DISPERSION 423
APPENDIX K ANSWERS TO SELECTED EXERCISES 429
REFERENCES 435
INDEX 439 |
| any_adam_object | 1 |
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| author_facet | Helrich, Carl S. |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.141 |
| dewey-search | 530.141 |
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| discipline | Physik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| spelling | Helrich, Carl S. Verfasser (DE-588)138804370 aut The classical theory of fields electromagnetism Carl S. Helrich Berlin [u.a.] Springer 2012 XIII, 446 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in Physics Elektromagnetismus (DE-588)4014306-5 gnd rswk-swf Feldtheorie (DE-588)4016698-3 gnd rswk-swf Feldtheorie (DE-588)4016698-3 s Elektromagnetismus (DE-588)4014306-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-23205-3 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3853534&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024512837&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Helrich, Carl S. The classical theory of fields electromagnetism Elektromagnetismus (DE-588)4014306-5 gnd Feldtheorie (DE-588)4016698-3 gnd |
| subject_GND | (DE-588)4014306-5 (DE-588)4016698-3 |
| title | The classical theory of fields electromagnetism |
| title_auth | The classical theory of fields electromagnetism |
| title_exact_search | The classical theory of fields electromagnetism |
| title_full | The classical theory of fields electromagnetism Carl S. Helrich |
| title_fullStr | The classical theory of fields electromagnetism Carl S. Helrich |
| title_full_unstemmed | The classical theory of fields electromagnetism Carl S. Helrich |
| title_short | The classical theory of fields |
| title_sort | the classical theory of fields electromagnetism |
| title_sub | electromagnetism |
| topic | Elektromagnetismus (DE-588)4014306-5 gnd Feldtheorie (DE-588)4016698-3 gnd |
| topic_facet | Elektromagnetismus Feldtheorie |
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