Classical Electrodynamics

Title page A Basic Equations 1 Basic Equations of Electrodynamics 1.a Charges and Currents 1.a.α Charge Density 1.a.η Current and Current Density 1.aγ Conservation of Charge and Equation of Continuity 1.b MAXWELL's Equations 1.c COULOMB and LORENTZ Force 2 Dimensions and Units 2.a Gaussian Units 2.b Other Systems of Units 2.c Motivation for Gaussian Units B Electrostatics 3 Electric Field, Potential, Energy of the Field 3.a Statics 3.b Electric Field and Potential 3.b.α Electric Potential 3.b.β Electric Flux and Charge 3.b.γ Potential of a Charge Distribution 3.c COULOMB Force and Field Energy 4 Electric Dipole and Quadrupole 4.a The Field for r > R 4.b Transformation Properties 4.c Dipole 4.d Quadrupole 4.d.α Symmetries 4.d.β Symmetric Quadrupole 4.e Energy, Force and Torque on a Multipole in an extemal Field 5 Multipole Expansion in Spherical Coordinates 5.a POISSON Equation in Spherical Coordinates 5.a.α The Gradient 5.a.β The Divergence 5.a.γ The Laplacian 5.b Spherical Harmonics 5.c Radial Equation and Multipole Moments 5.d Point Charge at r'. Cylindric Charge Distribution 6 Electric Field in Matter 6.a Polarization and Dielectric Displacement 6.b Boundaries between Dielectric Media 6.c Dielectric Sphere in a Homogeneous Electric Field 6.d Dielectric Constant according to CLAUSIUS and MOSSOTTI 7 Electricity on Conductors 7.a Electric Conductors 7.a.α Boundary Conditions at the Surface of the Conductor 7.a.β Force acting on the Conductor (in Vacuo) 7.b Capacities 7.c Influence Charges 7.c.a\apha Space free of Conductors 7.c.β Conducting Plane 7.c.γ Conducting Sphere 8 Energy, Forces and Stress in Dielectric Media 8.a Electrostatic Energy 8.b Force Density in Isotropic Dielectric Matter 8.c MAXWELL'S Stress Tensor C Magnetostatics 9 Magnetic Induction and Vector Potential 9.a AMPERE'S Law 9.b Magnetic Flux 9.c Field of a Current Distribution 9.d Vector Potential 9.e Force Between Two Circuits 10 Loops of Current as Magnetic Dipoles 10.a Localized Current Distribution and Magnetic Dipole 10.b Magnetic Dipolar Moment of a Current Loop 10.c Force and Torque on a Dipole in an External Magnetic Field 10.c.α Force 10.c.β Torque 11 Magnetism in Matter. Field of a Coil 11.a Magnetism in Matter 11.b Field of a coil D Law of Induction 12 FARADAY'S Law of Induction 13 Inductances and Electric Circuits 13.a Inductances 13.b Elements of Circuits 13.c KIRCHHOFF'S Rules 13.d Energy of Inductances 13.d.α Constant Inductances 13.d.β Moving Loops of CUfrents 13.d.γ Constant Magnetic Fluxes 13.d.δ Force between two Electric Circuits 13.d.ε Energy of a Magnetic Dipole in an External Magnetic Induction 13.d.ζ Permanent Magnetic Moments E MAXWELL'S Equations 14 Complete Set of MAXWELL'S Equations 14.a Consistency of MAXWELL'S Equations 14.b MAXWELL'S Equations for Freely Moving Charges and Currents 15 Energy and Momentum Balance 15.a Energy 15.b Momentum Balance F Electromagnetic Waves 16 Electromagnetic Waves in Vacuum and in Homogeneous Isotropic Insulators 16.a Wave Equation 16.b Plane Waves 16.c Superposition of Plane Periodic Waves 16.c.\apha Insertion on FOURIER Series and IntegraIs 16.c.β Back to MAXWELL'S Equations 16.c.γ Time averages and time integrals 17 Electromagnetic Waves in Homogeneous Conductors 17.a Transverse Oscillations at Low Frequencies 17.b Transverse Oscillations at High Frequencies 17.c Longitudinal = Plasma Oscilations 18 Reflection and Refraction at a Planar Surface 18.a Problem and Direction of Propagation 18.b Boundary Conditions, Amplitudes 18.c Discussion for μ_l = μ2 18.c.α Insulator, |sinα1| 1: Total Reflection 18.c.γ Metallic Reflection, α = 0 18.c.δ Surface Waves along a Conductor 19 Wave Guides 19.a Wave Guides 19.b Solution for a Rectangular Cross Section 19.c Wave Packets G Electrodynamic Potentials 20 Electrodynamic Potentials, Gauge Transformations 20.a Potentials 20.b Gauge Transformations 21 Electromagnetic Potentials of a general Charge and Current Distribution 21.a Ca1culation of the Potentials 21.b Gauge Condition 22 Radiation from Harmonic Oscillations 22.a Radiation Field 22.a.α Near Zone (Static Zone) 22.a.β Far Zone (Radiation Zone) 22.b Electric Dipole Radiation (HERTZ Dipole) 22.c Magnetic Dipole radiation and Electric Quadrupole Radiation 22.cα Magnetic Dipole Radiation 22.c.β Electric Quadrupole Radiation H LORENTZ Invariance of Electrodynamics 23 LORENTZ Transformation 23.a GAULEI and LORENTZ Transformation 23.b LORENTZ Transformation 23.b.α Time Dilatation 23.b.β LORENTZ Contraction 24 Four-Scalars and Four-Vectors 24.a Distance and Proper Time as Four-Scalars 24.a.α Space-like distance s2 0 24.a.γ Light-like distance s2 = 0 24.b World Velocity as Four-Vector 24.c Current Density Four-Vector 24.d Four-Potential 2S Electromagnetic Field Tensor 25.a Field Tensor 25.b MAXWELL'S Equations 25.b.α The Inhomogeneous Equations 25.b.β The Homogeneous Equations 25.c Transformation of the Electric and Magnetic Fields 25.d Fields of a Point Charge in Uniform Motion 25.e DOPPLER Effect 26 Relativistic Mechanics 26.a LORENTZ Force Density 26.b LORENTZ Force Acting on a Point Charge 26.c Energy and Momentum of a Mass Point 26.d Equation of Motion 27 Lagrangian Formulation 27.a Lagrangian of a Massive Charge in the Electromagnetic Field 27.b Lagrangian Density of the Electromagnetic Field 28 Energy Momentum Tensor and Conserved Quantities 28.a The Tensor 28.b Conservation Laws 28.b.α Charge 28.b.β Energy and Momentum 28.b.γ Angular Momentum and Movement of Center of Mass 29 Field of an arbitrarily Moving Point-Charge 29.a LIÉNARD-WIECHERT Potential 29.b The Fields 29.c Uniform Motion 29.d Accelerated Charge Momentarily at Rest 29.e Emitted Radiation, β ≠ 0 I Review and Outlook 30 Short History of Electrodynamics 30.a Theory of Light to FRESNEL 30.b Electrostatics 30.c Magnetostatics 30.d Set out for Electrodynamics 30.e Electrodynamics and Waves 30.f Theory of Relativity 30.g From Classical to Quantum Electrodynamics 31 Gravitational Time Dilatation 31.a Light Quantum in the Gravitational Field 31.b Principle of Equivalence Appendices A Connection between different Systems of Units B Formulae for Vector Calculus B.a Vector Algebra B.a.α Summation Convention and Orthonormal Basis B.a.β Scalar Product B.a.γ Vector Product B.a.δ Multiple Products B.b Vector Analysis B.b.α Differentiation in Space, DeI Operator B.b.β Second Derivatives, Laplacian B.b.γ Derivatives of Products B.c Special Expressions B.d Integral Theorems B.d.α Line IntegraIs B.d.β Surface IntegraIs B.d.γ Volume IntegraIs B.d.δ Volume IntegraIs of Products B.e The Laplacian of 1/r and Related Expressions B.e.α The Laplacian of 1/r B.e.β Representation of a Vector Field as a Sum of an Irrotational and a Divergence-free Field C Spherical Harmonics C.a Eigenvalue Problem and Separation of Variables C.b Associated LEGENDRE Functions C.c Orthogonality and Normalization C.d Remark on Completeness Name Index Subject Index Contents