ISBN: 3-540-65448-8
TITLE: Fundamentals of Electromagnetism
AUTHOR: Lopez Davalos, Arturo; Zanette, Damian
TOC:

1. Historical Perspective of Electromagnetism 1
Further Reading 11
2. Relativistic Kinematics 13
2.1 Relativity in Classical Mechanics 13
2.2 Prerelativistic Observations 14
2.2.1 The MichelsonMorley Experiment (18811904) 15
2.2.2 The Aberration of Fixed Stars (1728) 16
2.2.3 Fizeau's Experiment (1865) 17
2.3 The Special Theory of Relativity 18
2.4 Reference Systems and Lorentz Transformations 20
2.4.1 Experiment I 20
2.4.2 Experiment II 21
2.4.3 Experiment III 22
2.4.4 Experiment IV 24
2.5 Properties of the Lorentz Transformations 26
2.6 Minkowski Diagrams 28
2.7 Interpretation of Prerelativistic Experiments 32
2.8 The Speed of Light: 16751983 32
Problems 34
References 36
Further Reading 36
3. Relativistic Dynamics 37
3.1 Conservation Laws. Relativistic Momentum 37
3.2 Relativistic Force, Work and Energy 39
3.3 Tensor Formulation of the Lorentz Transformations 41
3.4 Covariant Formulation of Mechanics 42
3.5 Relativistic Analytical Dynamics 44
Problems 48
References 50
Further Reading 50
4. Electrostatics 51
4.1 Properties of the Electric Charge 52
4.2 Electric Field 56
4.3 Electrostatic Potential 58
4.4 Examples of Potentials and Fields. Multipole Expansion 59
4.5 Electrostatic Energy 65
4.6 Variational Principle for Electrostatics 69
4.7 Classical Radius of the Electron 71
4.8 Current Relevance of Electrostatics 72
4.8.1 Electric Neutrality of Matter 72
4.8.2 Validity of Coulomb's Law 72
4.8.3 Control of Environmental Pollution 73
4.8.4 Optimization of Industrial Painting 73
4.8.5 Photocopying 73
Problems 74
References 77
Further Reading 77
5. The Poisson and Laplace Equations 79
5.1 The Poisson and Laplace Equations in Other Branches of Physics 79
5.2 Solution of Poisson's Equation. Green's Function 81
5.3 Separation of Variables 86
5.3.1 Cartesian Coordinates 86
5.3.2 Spherical Coordinates 89
5.4 The Finite Element Method 92
Problems 96
References 99
Further Reading 100
6. Magnetic Field 101
6.1 Amp ere's Law 102
6.2 Vector Potential. The BiotSavart Law 104
6.3 Examples of Potentials and Fields. Multipole Expansion 106
6.4 Magnetic Energy. Variational Principle 110
6.5 Induction Coefficients 113
6.6 Symmetry Between Electrostatics and Magnetostatics 116
6.7 Problems of Current Interest in Magnetism 117
6.7.1 Earth's Magnetic Field 117
6.7.2 Isotope Separation 118
6.7.3 Particle Acceleration 118
6.7.4 Motors 119
6.7.5 The Existence of Monopoles 119
Problems 119
References 123
Further Reading 123
7. Maxwell's Equations 125
7.1 Time-Dependent Magnetic Fields. Faraday's Law 125
7.2 Displacement Current and Maxwell's Equations 127
7.3 Symmetries of Maxwell's Equations 129
7.3.1 Rotations 130
7.3.2 Space Reflection 131
7.3.3 Charge Inversion 133
7.3.4 Time Inversion 134
7.4 Electromagnetic Potentials and Gauge Transformations 135
7.4.1 Coulomb Gauge 136
7.4.2 Lorentz Gauge 138
7.5 Conservation Laws 138
7.6 Symmetries in Physics 142
Problems 143
References 145
Further Reading 146
8. Dynamic Fields and Radiation 147
8.1 Wave Propagation in Free Space 148
8.2 Green's Function for the Wave Equation 154
8.3 Fields of a Charge in Arbitrary Motion 156
8.4 Radiation Fields of a Moving Charge 158
8.5 Dipole Radiation 163
8.6 Inadequacy of the Planetary Model of the Atom 168
Problems 169
References 172
Further Reading 172
9. Covariant Formulation of Electromagnetism 173
9.1 Covariant Formulation of Potentials and Fields 173
9.2 Covariant Form of the Field of Charges and Dipoles 177
9.3 Lorentz Force and EnergyMomentum Tensor 179
9.4 Covariant Properties of the Free Radiation Field 180
9.5 Electromagnetic Theory of the Electron 183
9.6 A "Derivation" of Maxwell's Theory 185
Problems 188
References 190
Further Reading 190
10. Fields in Material Media 191
10.1 Macroscopic Fields 192
10.2 Sources of the Macroscopic Fields 198
10.3 Interfaces and Boundary Conditions 200
10.4 Electromagnetic Energy in Material Media 201
Problems 202
References 204
Further Reading 204
11. Linear Material Media 205
11.1 Linear Dielectrics 205
11.2 Polarization of Spherical and Ellipsoidal Bodies 206
11.3 Local Field in a Dielectric 211
11.4 Linear Magnetic Media 216
11.5 Linear Conducting Media 219
11.6 Variational Principle for Conducting Media 222
Problems 223
Further Reading 225
12. Waves in Material Media 227
12.1 Wave Equations in Linear Media 227
12.2 Waves at an Interface 230
12.3 Waves in Conducting Media 237
12.4 Polarization as Source of the Wave Fields 238
12.5 General Properties of the Linear Response 240
12.6 Lorentz Model for the Electric Susceptibility 243
Problems 247
References 249
Further Reading 250
13. Electromagnetic Theory of Superconductivity 251
13.1 Phenomenology 251
13.2 The London Theory 256
13.3 Magnetization and H-Field in a Superconductor 260
13.4 Application of the London Theory: Sphere in a Uniform Field 262
13.5 Flux Quantization 264
13.6 Energy of a Superconductor in a Magnetic Field 266
13.7 Present Relevance of Superconductivity 269
Problems 269
References 271
Further Reading 271
Appendix
A. The Dirac Delta Distribution 273
B. Legendre Polynomials and Spherical Harmonics 275
C. Covariant Notation and Tensor Calculus 279
D. Vector Identities, Theorems and Operators 283
E. Operation of PhysicSolver 285
Index 289
END
