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: Refraction
18.c.β Insulator, |sinα₂| > 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.β Time-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