Introduction to Classical Electrodynamics 3

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 Waveguides 11.1. The different types of waveguides 11.2. Description of a guided wave 21.2.1. Propagation equation and field expressions 21.2.2. Classification of propagation modes 61.3. TE and TM modes in a hollow conducting waveguide 81.3.1. Rectangular waveguide 91.3.2. Attenuation coefficient in a lossy waveguide 241.3.3. Propagation between two parallel planes 291.3.4. Cylindrical waveguide 331.4. Dielectric waveguides 371.4.1. Propagation between two parallel dielectric planes 371.4.2. Step index optical fiber 441.4.3. Modes with azimuthal symmetry 451.4.4. Modes with azimuthal dependence 481.4.5. Propagation modes in weakly guiding fibers 541.5. Resonant cavities 591.5.1. Rectangular metallic resonant cavity 601.5.2. Cylindrical resonant cavity 65Chapter 2 Transmission Lines 712.1. Parallel-plate transmission line 712.2. General formulation 732.3. Modeling of lossless transmission lines 782.4. Modeling of a transmission line with losses 792.5. Wave equations and sinusoidal solutions 822.6. Effects of losses in transmission lines 862.6.1. Low-loss limit 872.6.2. Distortionless lines 872.6.3. Solutions with arbitrary impedance at the line output 882.7. Resonance effect in a transmission line 942.8. Energy aspect in a transmission line 95Chapter 3 Electromagnetic Radiation 993.1. Retarded potentials 993.1.1. Inhomogeneous wave equations 993.1.2. Solutions of the inhomogeneous wave equations 1013.1.3. Solutions by Fourier analysis 1023.2. Radiation from a localized oscillating source 1063.2.1. Radiation from an electric dipole 1133.2.2. Radiations from the magnetic moment and the electric quadrupole 1193.2.3 Multipole radiation of order l ≥ 2 1273.2.4. Energy and angular momentum of multipolar fields 1323.3. Radiation from an extended source 135Chapter 4 Radiation from Point Charges 1454.1. Lińard–Wiechert potentials 1454.2. Fields of a moving point charge 1474.3. Radiation from a charge in uniform motion 1524.4. Radiation from a slowly moving charge 1534.5. Radiation from a relativistic charge 1544.5.1. Velocity and acceleration parallel 1554.5.2. Acceleration perpendicular to velocity 1584.5.3. General case 1664.6. Frequency distribution of the radiated energy 1704.7. Charge in instantaneous circular motion 1774.8. Particle in circular motion 1834.9. Thomson scattering of radiation 1884.10. Cherenkov radiation 196Chapter 5 Kirchhoff Diffraction 2015.1. Initial value problem: Kirchhoff’s integral representation 2015.1.1. Green’s function for the time-dependent wave equation 2015.1.2. Cauchy problem 2045.1.3. Poisson solution 2055.1.4. Kirchhoff representation of the field 2065.2. Kirchhoff integral for diffraction 2075.3. Vector form of the Kirchhoff integral 2125.4. Babinet’s principle of complementary screens 2175.5. Diffraction by a circular aperture 2205.6. Scattering by a conducting sphere in the short-wavelength limit 231Chapter 6 Theory of Special Relativity 2416.1. Postulates of special relativity and Lorentz transformation 2416.2. FitzGerald–Lorentz length contraction, time dilation and proper time 2486.3. Law of addition of velocities 2506.4. Four-dimensional Formalism 2556.4.1. Brehme–Lorentz diagram 2556.4.2. Transformations and Lorentz group 2596.4.3. Contravariant coordinates 2626.4.4. Covariant coordinates 2636.4.5. Change of basis 2646.4.6. Four-velocity, four-momentum and four-acceleration 2666.4.7. Tensors 2696.4.8. Differentiation, vector analysis and integration 2726.5. Relativistic dynamics 2746.5.1. Relativistic Lagrangian for a free particle 2746.5.2. Four-momentum 2756.5.3. Application to collisions 2786.5.4. Minkowski four-force 280Chapter 7 Covariant Formulation 2857.1. A brief remark on field theory 2857.1.1. Transition from a discrete system to a continuous one 2857.1.2. Continuous system 2867.1.3. Euler–Lagrange equations 2877.1.4. Hamiltonian formalism 2887.1.5. Gauge invariance 2907.1.6. Infinitesimal symmetry 2917.1.7. Energy–momentum tensor of a field 2927.1.8. Angular momentum tensor 2937.1.9. Electromagnetic interaction 2937.2. Free particle in a field 2947.2.1. Four-potential 2947.2.2. Equation of relativistic dynamics 2967.2.3. Electromagnetic field tensor 2987.2.4. Lorentz force 3007.2.5. Change of reference frames for the field 3027.2.6. Invariants of the electromagnetic field 3057.2.7. First group of Maxwell equations 3067.3. Sources of the field: second group of Maxwell equations 3077.3.1. Interaction between a field and a current 3087.3.2. Free field action (field self-interaction) 3097.3.3. Magnetization and polarization 3117.4. Energy–momentum tensor 3127.4.1. Conservation law 3147.4.2. Time component: conservation of energy 3157.4.3. Spatial components: conservation of momentum 3167.5. Electromagnetic mass 3187.6. Radiation reaction force from energy balance 3217.7. Abraham–Lorentz model 3257.8. Abraham–Lorentz equation of motion 3327.9. Dirac radiation equation 3347.10 And the story continues 335References 337Index 343