Advanced Electromagnetic Theory

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