Advanced Electromagnetic Theory, 1st ed. 2022 Lecture Notes in Physics Series, Vol. 1009

Chapter 1. Introduction
Lecture 1 — Possibility of axiomatic formulation of electromagnetic Theory.
Basic equations, separation into electrostatics and magnetostatics in the absence
Chapter 2. Electrostatics
Lecture 2 — Electrostatic equations, electrostatic potential, Coulomb’s law,
Poisson’s equation. Potential and electric field due to a dipole and a uniform
dipole surface. Gauss’s theorem and applications.
Lecture 3 — Curvilinear coordiates, the Laplacian in cylindrical and spherical
coordinates. Uniqueness theorem for Laplace’s equation. Method of images,
point charge in front of plane surface and sphere.
Lecture 4 — Boundary value problems in two-dimensional Cartesian and
polar geometry, general solutions and specific examples.
Lecture 5 — Boundary value problems in axisymmetric spherical geometry,
Legendre polynomials. Multipole expansion for an axisymmetric distribution of
charges.
Lecture 6—Dielectric medium: electric polarization, basic equations, boundary
conditions. Dielectric sphere in uniform electric field. Energy density of
Chapter 3. Magnetostatics
Lecture 7 — Basic equations, vector potential, Biot-Savart law, Ampere’s law.
Techniques for solving magnetostatic problems. Magnetic field due to localized
currents.
Lecture 8 — Multipole expansion of magnetostatic fields, magnetic moment.
Chapter 4. Electrodynamics and Electromagnetic
Waves
Lecture 9 — Maxwell’s equations, charge conservation, significance of Faraday’s
law of electomagnetic induction. Energy and momentum of electromagnetic
fields, electromagnetic field tensor.
Lecture 10 — Electromagnetic waves in non-conducting medium, polarization,
Stokes parameters. Electromagnetic waves in conducting medium, skin
depth.
Lecture 11 — Reflection and refraction at an interface between two media,
Fresnel formulae, Brewster’s law, total internal reflection.
Lecture 12 — Rectangular wave guides, interior equations and boundary
Chapter 5. Relativity and Electrodynamics
Lecture 13 — Lorentz transformation, transformation of velocities, aberration
of light. Introduction to tensors. Special relativity in 4-vector notation, Doppler
effect.
Lecture 14 — Relativistic mechanics, velocity 4-vector and 4-momentum.
Covariant formulation of electrodynamics, 4-potential, electromagnetic field tensor,
Maxwell’s equations in covariant notation.
Lecture 15 — Transformation of electromagnetic fields, Lorentz 4-force. Action
Chapter 6. Electrodynamics of Moving Charges
Lecture 16 — Gauge freedom, Lorentz gauge, inhomogeneous wave equation.
Solution of inhomogeneous equations by Green’s function.
Lecture 17 — Retarded potential, Lienard–Wiechert potential. Calculation
of the electromagnetic field due to a moving charge.
Lecture 18— Electromagnetic radiation emitted by accelerated charges, Larmor’s
formula. Radiation from oscillating currents, centre-fed linear antenna.
Dipole approximation in radiation emission.
Lecture 19 — Radiation from oscillating dipole. Thomson scattering due to
free electrons. Radiation reaction.
Lecture 20 — Harmonically bound electrons and Rayleigh scattering. Relativistic
Chapter 7. Plasma Physics
Lecture 21 — Different approaches to plasma physics. Debye shielding and
quasi-neutrality. Electromagnetic oscillations in cold plasmas, plasma frequency,
propagation of electromagnetic waves.
Lecture 22 — The MHD approximation, basic equations of MHD, induction
equation. Significance of magnetic Reynolds number, theorem of flux freezing,
applications to astrophysics.
Lecture 23 — Plasma confinement with magnetic fields in cylindrical geometry,
qualitative introduction to plasma instabilities. MHD waves in uniformly
magnetized plasma.