Preface ix
Chapter 1 Static Potentials with Sources 1
1.1. Poisson equation 1
1.2. The image charge method 6
1.2.1. General properties 6
1.2.2. Point charge in proximity to a conducting plane 7
1.2.3. Point charge in proximity to a conducting sphere 15
1.2.4. Dipole in proximity to a conducting sphere 23
1.2.5. Infinite line charge in proximity to a plane 26
1.2.6. Infinite line charge in proximity to a conducting cylinder 27
1.3. Green’s function 34
1.3.1. Position of the problem 34
1.3.2. Poisson equation solutions 34
1.3.3. Green’s theorem 36
1.3.4. Inverse Laplacian and Green’s function 36
1.3.5. Derivation of the Green’s function by the Fourier transform 39
1.4. Integral form of the Poisson equation 40
1.5. Expansion of Green’s function on spherical harmonics 43
1.6. Green–Dirichlet function from its differential equation 49
1.7. Eigenfunctions method 55
Chapter 2 Electromagnetic Induction Phenomena 59
2.1. Experimental observations 59
2.2. EMF for static fields (Lorentz case) 66
2.3. Variable magnetic field (Neumann case) 71
VI Introduction to Classical Electrodynamics 2
2.3.1. Motion relative to the fixed reference Oxyz 71
2.3.2. Motion Relative to the Moving Frame O ′ X ′ Y ′ Z ′ Attached to the circuit 73
2.3.3. Maxwell–Faraday equation 75
2.4. General case of a deformable circuit 76
2.4.1. Electromotive field and induced EMF 76
2.4.2. Faraday’s law 76
2.5. Maxwell–Ampere equation and displacement current 81
2.6. Lorentz force and canonical momentum 85
2.7. Maxwell equations 88
2.8. Gauge transformations 88
Chapter 3 Electromagnetic Waves in a Vacuum 95
3.1. Wave equations in a vacuum 95
3.2. One-dimensional solutions 98
3.3. Structure of a plane electromagnetic wave 102
3.4. Progressive plane monochromatic waves (PPMW) 104
3.4.1. Sinusoidal solutions of the d’Alembert propagation equation 104
3.4.2. Complex representation of PPMWs 111
3.4.3. Polarization of a PPMW 113
3.5. Interference of light waves 124
3.6. Transverse electric (TE) and transverse magnetic (TM) spherical waves 132
Chapter 4 Electromagnetic Energies 137
4.1. Energy stored in a charged distribution 137
4.1.1. Electrostatic potential energy of a distribution of point charges 138
4.1.2. Electrostatic energy of a continuous charge distribution 143
4.1.3. Energy stored in the electric field 147
4.1.4. Electrostatic interaction energy between two fields 150
4.2. Electrostatic actions on a conductor in equilibrium 153
4.2.1. Concepts of rigid body mechanics 153
4.2.2. Electrostatic actions from electrostatic energy 155
4.3. Magnetic actions 159
4.3.1. Laplace force – Moment of Laplace force 159
4.3.2. Magnetic moment of a closed circuit in a constant magnetic field 160
4.3.3. Expressions of actions from magnetic energy 161
4.4. Action of a magnetic field on a conductor: magnetoresistance 163
4.5. Magnetic inductances 166
4.5.1. Neumann formula 166
4.5.2. Inductance matrix 170
4.5.3. Mutual inductance coupling 175
4.6. Electromagnetic energy 184
4.6.1. Magnetic energy of a set of n thin-wire circuits 184
4.6.2. Magnetic energy of a volume current distribution 184
4.6.3. Poynting’s theorem 190
4.7. Maxwell tensor 194
4.7.1. Maxwell stress tensor for the electric field 194
4.7.2. Maxwell stress tensor for the magnetic field 197
4.7.3. Maxwell stress tensor for the electromagnetic field 199
4.7.4. Eigenvalues of the electromagnetic stress tensor 200
4.8. Magnetic monopoles and dual transformations 201
Chapter 5 Polarization, Polarized Media (Dielectrics) 205
5.1. Polarization vector (field), polarization charge 205
5.2. Electric field created by a dielectric 208
5.3. Boundary conditions for −→ E and bound surface charge density 210
5.4. Electric displacement field 219
5.5. Microscopic approach to linear dielectric media 220
5.5.1. Electronic polarization in steady-state 221
5.5.2. Electric polarization in a time-varying regime 224
5.5.3. Ionic polarization 228
5.5.4. Orientation polarization of polar molecules 230
5.6 Boundary conditions for the field −→ D 235
5.7. Polarization current 249
5.8. Kramers–Kronig relations 250
Chapter 6 Magnetization, Magnetized Media 257
6.1. Magnetic field generated by magnetized medium: macroscopic description 257
6.1.1. Magnetization vector field 257
6.1.2. Magnetization current 260
6.1.3. Vector potential and macroscopic magnetic field 262
6.1.4 Magnetic excitation vector −→ H 264
6.1.5 Boundary conditions for the fields −→ B and −→ H 265
6.2. Microscopic description of magnetization 275
6.2.1. Problem statement 275
6.2.2. Diamagnetism 276
6.2.3. Paramagnetism 282
6.2.4. Ferromagnetism 288
6.3. Constitutive relations 291
6.3.1. Linear magnetic medium 291
6.3.2. Calculation of induced magnetization 292
6.3.3 Calculation of −→ H and −→ B in a magnetized medium (given −→ M) 301
6.4. Method of images 306
6.4.1. Image of a magnetic moment in an infinitely permeable medium 306
6.4.2. Image of a current line 308
6.5. Magnetic field and force 311
Chapter 7 Electromagnetic Fields in Matter 321
7.1. Maxwell equations 321
7.2. Energy conservation 329
7.2.1. Electrostatic energy stored in a charge distribution 329
7.2.2. Poynting vector 330
7.2.3. Electromagnetic momentum and Maxwell stress tensor 334
7.2.4. Complex Poynting theorem 336
7.3. Electromagnetic potentials 338
7.4. Plane wave in material medium 339
7.4.1. Plane wave in a linear and isotropic dielectric 341
7.4.2. Electromagnetic wave in a conductive medium 350
7.4.3. Propagation of an electromagnetic wave in a plasma 355
7.4.4. Propagation in a dielectric medium 360
7.5. Dispersive media 366
7.5.1. Propagation in a dispersive and absorbent medium 369
7.5.2. Propagation in a transparent and inhomogeneous medium 371
7.6. Normal incidence on a perfect conductor 376
7.7. Normal incidence on a dielectric 378
7.7.1. Lossless (perfect) dielectric 378
7.7.2. Dielectric with losses (with ohmic conductivity) 380
7.7.3. Complete signal transmission through a coating 381
7.8. Oblique incidence of a plane wave 383
7.8.1. Oblique incidence on a perfect conductor 388
7.8.2. Oblique incidence on a perfect dielectric 390
References 401
Index 407
