Introduction to Electrodynamics

Cover......Page 1
Title page......Page 2
Edition notice......Page 3
Contents......Page 4
Preface......Page 10
Advertisement......Page 12
1.1.1 Vector Operations......Page 18
1.1.2 Vector Algebra: Component Form......Page 21
1.1.3 Triple Products......Page 24
1.1.4 Position, Displacement, and Separation Vectors......Page 25
1.1.5 How Vectors Transform......Page 27
1.2.2 Gradient......Page 30
1.2.3 The Operator ∇......Page 33
1.2.4 The Divergence......Page 34
1.2.5 The Curl......Page 36
1.2.6 Product Rules......Page 37
1.2.7 Second Derivatives......Page 39
1.3.1 Line, Surface, and Volume Integrals......Page 41
1.3.2 The Fundamental Theorem of Calculus......Page 45
1.3.3 The Fundamental Theorem for Gradients......Page 46
1.3.4 The Fundamental Theorem for Divergences......Page 48
1.3.5 The Fundamental Theorem for Curls......Page 51
1.3.6 Integration by Parts......Page 54
1.4.1 Spherical Polar Coordinates......Page 55
1.4.2 Cylindrical Coordinates......Page 60
1.5.1 The Divergence of r̂/r²......Page 62
1.5.2 The One-Dimensional Dirac Delta Function......Page 63
1.5.3 The Three-Dimensional Delta Function......Page 67
1.6.1 The Helmholtz Theorem......Page 69
1.6.2 Potentials......Page 70
2.1.1 Introduction......Page 75
2.1.2 Coulomb’s Law......Page 76
2.1.3 The Electric Field......Page 77
2.1.4 Continuous Charge Distributions......Page 78
2.2.1 Field Lines, Flux, and Gauss’s Law......Page 82
2.2.2 The Divergence of E......Page 86
2.2.3 Applications of Gauss’s Law......Page 87
2.2.4 The Curl of E......Page 93
2.3.1 Introduction to Potential......Page 94
2.3.2 Comments on Potential......Page 96
2.3.4 The Potential of a Localized Charge Distribution......Page 100
2.3.5 Summary; Electrostatic Boundary Conditions......Page 104
2.4.1 The Work Done to Move a Charge......Page 107
2.4.2 The Energy of a Point Charge Distribution......Page 108
2.4.3 The Energy of a Continuous Charge Distribution......Page 110
2.4.4 Comments on Electrostatic Energy......Page 112
2.5.1 Basic Properties......Page 113
2.5.2 Induced Charges......Page 115
2.5.3 Surface Charge and the Force on a Conductor......Page 119
2.5.4 Capacitors......Page 120
3.1.1 Introduction......Page 127
3.1.2 Laplace’s Equation in One Dimension......Page 128
3.1.3 Laplace’s Equation in Two Dimensions......Page 129
3.1.4 Laplace’s Equation in Three Dimensions......Page 131
3.1.5 Boundary Conditions and Uniqueness Theorems......Page 133
3.1.6 Conductors and the Second Uniqueness Theorem......Page 135
3.2.1 The Classic Image Problem......Page 138
3.2.3 Force and Energy......Page 140
3.2.4 Other Image Problems......Page 141
3.3.1 Cartesian Coordinates......Page 144
3.3.2 Spherical Coordinates......Page 154
3.4.1 Approximate Potentials at Large Distances......Page 163
3.4.2 The Monopole and Dipole Terms......Page 166
3.4.3 Origin of Coordinates in Multipole Expansions......Page 168
3.4.4 The Electric Field of a Dipole......Page 170
4.1.1 Dielectrics......Page 177
4.1.2 Induced Dipoles......Page 178
4.1.3 Alignment of Polar Molecules......Page 181
4.2.1 Bound Charges......Page 183
4.2.2 Physical Interpretation of Bound Charges......Page 187
4.2.3 The Field Inside a Dielectric......Page 190
4.3.1 Gauss’s Law in the Presence of Dielectrics......Page 192
4.3.3 Boundary Conditions......Page 195
4.4.1 Susceptibility, Permittivity, Dielectric Constant......Page 196
4.4.2 Boundary Value Problems with Linear Dielectrics......Page 203
4.4.3 Energy in Dielectric Systems......Page 208
4.4.4 Forces on Dielectrics......Page 210
5.1.1 Magnetic Fields......Page 219
5.1.2 Magnetic Forces......Page 221
5.1.3 Currents......Page 225
5.2.2 The Magnetic Field of a Steady Current......Page 232
5.3.1 Straight-Line Currents......Page 238
5.3.2 The Divergence and Curl of B......Page 239
5.3.3 Applications of Ampère’s Law......Page 242
5.3.4 Comparison of Magnetostatics and Electrostatics......Page 249
5.4.1 The Vector Potential......Page 251
5.4.2 Summary; Magnetostatic Boundary Conditions......Page 257
5.4.3 Multipole Expansion of the Vector Potential......Page 259
6.1.2 Torques and Forces on Magnetic Dipoles......Page 272
6.1.3 Effect of a Magnetic Field on Atomic Orbits......Page 277
6.1.4 Magnetization......Page 279
6.2.1 Bound Currents......Page 280
6.2.2 Physical Interpretation of Bound Currents......Page 283
6.2.3 The Magnetic Field Inside Matter......Page 285
6.3.1 Ampère’s law in Magnetized Materials......Page 286
6.3.3 Boundary Conditions......Page 290
6.4.1 Magnetic Susceptibility and Permeability......Page 291
6.4.2 Ferromagnetism......Page 295
7.1.1 Ohm’s Law......Page 302
7.1.2 Electromotive Force......Page 309
7.1.3 Motional emf......Page 311
7.2.1 Faraday's Law......Page 318
7.2.2 The Induced Electric Field......Page 322
7.2.3 Inductance......Page 327
7.2.4 Energy in Magnetic Fields......Page 334
7.3.1 Electrodynamics Before Maxwell......Page 338
7.3.2 How Maxwell Fixed Ampère’s Law......Page 340
7.3.3 Maxwell’s Equations......Page 343
7.3.4 Magnetic Charge......Page 344
7.3.5 Maxwell’s Equations in Matter......Page 345
7.3.6 Boundary Conditions......Page 348
8.1.1 The Continuity Equation......Page 362
8.1.2 Poynting’s Theorem......Page 363
8.2.1 Newton’s Third Law in Electrodynamics......Page 366
8.2.2 Maxwell’s Stress Tensor......Page 368
8.2.3 Conservation of Momentum......Page 372
8.2.4 Angular Momentum......Page 375
9.1.1 The Wave Equation......Page 381
9.1.2 Sinusoidal Waves......Page 384
9.1.3 Boundary Conditions: Reflection and Transmission......Page 387
9.1.4 Polarization......Page 390
9.2.1 The Wave Equation for E and B......Page 392
9.2.2 Monochromatic Plane Waves......Page 393
9.2.3 Energy and Momentum in Electromagnetic Waves......Page 397
9.3.1 Propagation in Linear Media......Page 399
9.3.2 Reflection and Transmission at Normal Incidence......Page 401
9.3.3 Reflection and Transmission at Oblique Incidence......Page 403
9.4.1 Electromagnetic Waves in Conductors......Page 409
9.4.2 Reflection at a Conducting Surface......Page 413
9.4.3 The Frequency Dependence of Permittivity......Page 415
9.5.1 Wave Guides......Page 422
9.5.2 TE Waves in a Rectangular Wave Guide......Page 425
9.5.3 The Coaxial Transmission Line......Page 428
10.1.1 Scalar and Vector Potentials......Page 433
10.1.2 Gauge Transformations......Page 436
10.1.3 Coulomb Gauge and Lorentz* Gauge......Page 438
10.2.1 Retarded Potentials......Page 439
10.2.2 Jefimenko’s Equations......Page 444
10.3.1 Liénard-Wiechert Potentials......Page 446
10.3.2 The Fields of a Moving Point Charge......Page 452
11.1.1 What is Radiation?......Page 460
11.1.2 Electric Dipole Radiation......Page 461
11.1.3 Magnetic Dipole Radiation......Page 468
11.1.4 Radiation from an Arbitrary Source......Page 471
11.2.1 Power Radiated by a Point Charge......Page 477
11.2.2 Radiation Reaction......Page 482
11.2.3 The Physical Basis of the Radiation Reaction......Page 486
12.1.1 Einstein’s Postulates......Page 494
12.1.2 The Geometry of Relativity......Page 500
12.1.3 The Lorentz Transformations......Page 510
12.1.4 The Structure of Spacetime......Page 517
12.2.1 Proper Time and Proper Velocity......Page 524
12.2.2 Relativistic Energy and Momentum......Page 526
12.2.3 Relativistic Kinematics......Page 528
12.2.4 Relativistic Dynamics......Page 533
12.3.1 Magnetism as a Relativistic Phenomenon......Page 539
12.3.2 How the Fields Transform......Page 542
12.3.3 The Field Tensor......Page 552
12.3.4 Electrodynamics in Tensor Notation......Page 554
12.3.5 Relativistic Potentials......Page 558
A.2 Notation......Page 564
A.3 Gradient......Page 565
A.4 Divergence......Page 566
A.5 Curl......Page 569
A.6 Laplacian......Page 571
Appendix B The Helmholtz Theorem......Page 572
Appendix C Units......Page 575
Index......Page 579