Chapter 1. Introduction Lecture 1 -- Possibility of axiomatic formulation of electromagnetic Theory. Basic equations, separation into electrostatics and magnetostatics in the absence of time dependence. Solution of the general static equations, -function. 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 electrostatic fields. 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. Magnetic medium, ferromagnetism, example of uniformly magnetized sphere. 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 conditions, TE and TM modes. Rectangular cavity resonator. 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 of charged particle in electromagnetic field, Lagrangian formulation of electrodynamics. 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 beaming and synchrotron radiation. Bremsstrahlung. 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.