A Modern Introduction to Classical Electrodynamics is suitable for undergraduate students with some background knowledge of the subject and for graduate students, while more advanced topics make it a useful resource for PhD students and researchers.
The book places much emphasis on the formal structure of the theory; beginning with Maxwell's equations in the vacuum, it emphasises the central role of gauge invariance and Special Relativity. After introductory chapters which include rederivations of elementary results of electrostatics and magnetostatics, and the multipole expansion, Special Relativity is introduced, and most of the subsequent derivations are performed using covariant formalism and gauge potentials, allowing for greater conceptual and technical clarity compared to more traditional treatments.
The second part of the book covers electrodynamics in material media. This includes Maxwell's equations in material media, frequency dependent response of materials and Kramers-Kronig relations, electromagnetic waves in materials, and scattering of electromagnetic radiation. Finally, the text also includes advanced topics, such as the field-theoretical treatment of classical electrodynamics as a modern treatment of radiation reaction. These parts are meant for the advanced reader and are clearly marked, and can be skipped without loss of continuity.
Author(s): Michele Maggiore
Series: Oxford Master Series in Statistical, Computational and Theoretical Physics
Edition: 1
Publisher: Oxford University Press
Year: 2023
Language: English
Pages: 435
Tags: Maxwell Equations, Electrostatics, Magnetostatics, Electromagnetic Energy, Special Relativity, Covariant Formulation, Radiation, Scattering
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
