Introduction to Classical Electrodynamics 2

Boucif Abdesselam is a professor in the Physics Department of the Faculty of Science and Technology at the Université Ain Temouchent Belhadj Bouchai, Algeria. He is also a member of the Theoretical Physics Laboratory at the University of Oran 1, Algeria.

• Preface ixChapter 1 Static Potentials with Sources 11.1. Poisson equation 11.2. The image charge method 61.2.1. General properties 61.2.2. Point charge in proximity to a conducting plane 71.2.3. Point charge in proximity to a conducting sphere 151.2.4. Dipole in proximity to a conducting sphere 231.2.5. Infinite line charge in proximity to a plane 261.2.6. Infinite line charge in proximity to a conducting cylinder 271.3. Green’s function 341.3.1. Position of the problem 341.3.2. Poisson equation solutions 341.3.3. Green’s theorem 361.3.4. Inverse Laplacian and Green’s function 361.3.5. Derivation of the Green’s function by the Fourier transform 391.4. Integral form of the Poisson equation 401.5. Expansion of Green’s function on spherical harmonics 431.6. Green–Dirichlet function from its differential equation 491.7. Eigenfunctions method 55Chapter 2 Electromagnetic Induction Phenomena 592.1. Experimental observations 592.2. EMF for static fields (Lorentz case) 662.3. Variable magnetic field (Neumann case) 71VI Introduction to Classical Electrodynamics 22.3.1. Motion relative to the fixed reference Oxyz 712.3.2. Motion Relative to the Moving Frame O ′ X ′ Y ′ Z ′ Attached to the circuit 732.3.3. Maxwell–Faraday equation 752.4. General case of a deformable circuit 762.4.1. Electromotive field and induced EMF 762.4.2. Faraday’s law 762.5. Maxwell–Ampère equation and displacement current 812.6. Lorentz force and canonical momentum 852.7. Maxwell equations 882.8. Gauge transformations 88Chapter 3 Electromagnetic Waves in a Vacuum 953.1. Wave equations in a vacuum 953.2. One-dimensional solutions 983.3. Structure of a plane electromagnetic wave 1023.4. Progressive plane monochromatic waves (PPMW) 1043.4.1. Sinusoidal solutions of the d’Alembert propagation equation 1043.4.2. Complex representation of PPMWs 1113.4.3. Polarization of a PPMW 1133.5. Interference of light waves 1243.6. Transverse electric (TE) and transverse magnetic (TM) spherical waves 132Chapter 4 Electromagnetic Energies 1374.1. Energy stored in a charged distribution 1374.1.1. Electrostatic potential energy of a distribution of point charges 1384.1.2. Electrostatic energy of a continuous charge distribution 1434.1.3. Energy stored in the electric field 1474.1.4. Electrostatic interaction energy between two fields 1504.2. Electrostatic actions on a conductor in equilibrium 1534.2.1. Concepts of rigid body mechanics 1534.2.2. Electrostatic actions from electrostatic energy 1554.3. Magnetic actions 1594.3.1. Laplace force – Moment of Laplace force 1594.3.2. Magnetic moment of a closed circuit in a constant magnetic field 1604.3.3. Expressions of actions from magnetic energy 1614.4. Action of a magnetic field on a conductor: magnetoresistance 1634.5. Magnetic inductances 1664.5.1. Neumann formula 1664.5.2. Inductance matrix 1704.5.3. Mutual inductance coupling 1754.6. Electromagnetic energy 1844.6.1. Magnetic energy of a set of n thin-wire circuits 1844.6.2. Magnetic energy of a volume current distribution 1844.6.3. Poynting’s theorem 1904.7. Maxwell tensor 1944.7.1. Maxwell stress tensor for the electric field 1944.7.2. Maxwell stress tensor for the magnetic field 1974.7.3. Maxwell stress tensor for the electromagnetic field 1994.7.4. Eigenvalues of the electromagnetic stress tensor 2004.8. Magnetic monopoles and dual transformations 201Chapter 5 Polarization, Polarized Media (Dielectrics) 2055.1. Polarization vector (field), polarization charge 2055.2. Electric field created by a dielectric 2085.3. Boundary conditions for −→ E and bound surface charge density 2105.4. Electric displacement field 2195.5. Microscopic approach to linear dielectric media 2205.5.1. Electronic polarization in steady-state 2215.5.2. Electric polarization in a time-varying regime 2245.5.3. Ionic polarization 2285.5.4. Orientation polarization of polar molecules 2305.6 Boundary conditions for the field −→ D 2355.7. Polarization current 2495.8. Kramers–Krönig relations 250Chapter 6 Magnetization, Magnetized Media 2576.1. Magnetic field generated by magnetized medium: macroscopic description 2576.1.1. Magnetization vector field 2576.1.2. Magnetization current 2606.1.3. Vector potential and macroscopic magnetic field 2626.1.4 Magnetic excitation vector −→ H 2646.1.5 Boundary conditions for the fields −→ B and −→ H 2656.2. Microscopic description of magnetization 2756.2.1. Problem statement 2756.2.2. Diamagnetism 2766.2.3. Paramagnetism 2826.2.4. Ferromagnetism 2886.3. Constitutive relations 2916.3.1. Linear magnetic medium 2916.3.2. Calculation of induced magnetization 2926.3.3 Calculation of −→ H and −→ B in a magnetized medium (given −→ M) 3016.4. Method of images 3066.4.1. Image of a magnetic moment in an infinitely permeable medium 3066.4.2. Image of a current line 3086.5. Magnetic field and force 311Chapter 7 Electromagnetic Fields in Matter 3217.1. Maxwell equations 3217.2. Energy conservation 3297.2.1. Electrostatic energy stored in a charge distribution 3297.2.2. Poynting vector 3307.2.3. Electromagnetic momentum and Maxwell stress tensor 3347.2.4. Complex Poynting theorem 3367.3. Electromagnetic potentials 3387.4. Plane wave in material medium 3397.4.1. Plane wave in a linear and isotropic dielectric 3417.4.2. Electromagnetic wave in a conductive medium 3507.4.3. Propagation of an electromagnetic wave in a plasma 3557.4.4. Propagation in a dielectric medium 3607.5. Dispersive media 3667.5.1. Propagation in a dispersive and absorbent medium 3697.5.2. Propagation in a transparent and inhomogeneous medium 3717.6. Normal incidence on a perfect conductor 3767.7. Normal incidence on a dielectric 3787.7.1. Lossless (perfect) dielectric 3787.7.2. Dielectric with losses (with ohmic conductivity) 3807.7.3. Complete signal transmission through a coating 3817.8. Oblique incidence of a plane wave 3837.8.1. Oblique incidence on a perfect conductor 3887.8.2. Oblique incidence on a perfect dielectric 390References 401Index 407