A Modern Introduction to Classical Electrodynamics

Cover
Titlepage
Copyright
Dedication
Preface
Contents
1
Mathematical tools
	1.1 Vector algebra
	1.2 Di erential operators on scalar and vector elds
	1.3 Integration of vector elds. Gauss's and Stokes's theorems
	1.4 Dirac delta
	1.5 Fourier transform
	1.6 Tensors and rotations
	1.7 Groups and representations
2
Systems of units
	2.1 The SI system
	2.2 Gaussian units
	2.3 SI or Gaussian?
3
Maxwell's equations
	3.1 Maxwell's equations in vector form
	3.2 Conservation laws
	3.3 Gauge potentials and gauge invariance
	3.4 Symmetries of Maxwell's equations
4
Elementary applications of Maxwell's equations
	4.1 Electrostatics
	4.2 Magnetostatics
	4.3 Electromagnetic induction
	4.4 Solved problems
5
Electromagnetic energy
	5.1 Work and energy in electrostatics
	5.2 Energy stored in a static electric eld
	5.3 Work and energy in magnetostatics
	5.4 Energy stored in a static magnetic eld
	5.5 Forces and mechanical potentials
	5.6 Solved problems
6
Multipole expansion for static elds
	6.1 Electric multipoles
	6.2 Magnetic multipoles
	6.3 Point-like electric or magnetic dipoles
	6.4 Multipole expansion of interaction potentials
	6.5 Solved problems
7
Special Relativity
	7.1 The postulates
	7.2 Space and time in Special Relativity
	7.3 The mathematics of the Lorentz group
	7.4 Relativistic particle kinematics
8
Covariant formulation of electrodynamics
	8.1 The four-vector current
	8.2 The four-vector potential
	and the
	tensor
	8.3 Covariant form of Maxwell's equations
	8.4 Energy-momentum tensor of the electromagnetic eld
	8.5 Lorentz transformations of electric and magnetic elds
	8.6 Relativistic formulation of the particleeld interaction
	8.7 Field-theoretical approach to classical electrodynamics
	8.8 Solved problems
9
Electromagnetic waves in vacuum
	9.1 Wave equations
	9.2 Electromagnetic waves in the Lorenz gauge
	9.3 Electromagnetic waves in the Coulomb gauge
	9.4 Solutions for E and B
	9.5 Polarization of light
	9.6 Doppler e ect and light aberration
10
Electromagnetic eld of moving charges
	10.1 Advanced and retarded Green's function
	10.2 The Li enard{Wiechert potentials
	10.3 Fields of charge in uniform motion
	10.4 Radiation eld from accelerated charges
	10.5 Radiation from non-relativistic charges. Larmor formula
	10.6 Power radiated by relativistic sources
	10.7 Solved problems
11
Radiation from localized sources
	11.1 Far zone elds for generic velocities
	11.2 Low-velocity limit and multipole expansion of the radiation eld
	11.3 Near zone, far zone and induction zone
	11.4 Solved problems
12
Post-Newtonian expansion and radiation reaction
	12.1 Expansion for small retardation
	12.2 Dynamics to order
	12.3 Self-force and radiation reaction
13
Electromagnetic elds in material media
	13.1 Maxwell's equations for macroscopic elds
	13.2 The macroscopic charge density: free and bound charges
	13.3 The macroscopic current density
	13.4 Maxwell's equations in material media
	13.5 Boundary conditions on E, B, D, H
	13.6 Constitutive relations
	13.7 Energy conservation
	13.8 Solved problems
14
Frequency-dependent response of materials
	14.1 General properties of
	,
	14.2 Causality constraints and Kramers{Kronig relations
	14.3 The Drude{Lorentz model for
	14.4 The Drude model of conductivity
	14.5 The dielectric function of metals
15
Electromagnetic waves in material media
	15.1 Electromagnetic waves in dielectrics
	15.2 Phase velocity and group velocity
	15.3 Electromagnetic waves in metals
	15.4 Electromagnetic waves in waveguides
16
Scattering of electromagnetic radiation
	16.1 Scattering cross-section
	16.2 Scattering on a free electron
	16.3 Scattering on a bound electron
A
 Electrodynamics in Gaussian units
References
Index