MPH6163: Advanced Electromagnetism

The course is in two almost independent parts: Electrodynamics (Part 1) and Special Relativity (Part2)

Part 2 has already been taught by Prof. Gazeau. The syllabus is below.  Part I will be taught also. 

PART I: ELECTRODYNAMICS

Review of the Coulomb, Gauss’s laws and surface integral, Bio-Savart law, Ampere’s law and line integral, Faraday law. The Divergence Theorem. Conservation of charge and the equation of continuity. Stokes’ Theorem and the meaning of the curl. Simple examples of curl in cylindrical polar coordinates. The displacement current. A more comprehensive study of Lorentz force, Electrostatics, Magnetostatics and Faraday’s law. Maxwell’s equations (non-relativistic form). Conservation laws. Then solving Maxwell’s equations: Retarded solutions, Radiating Systems and Plane waves. This would include boundary problems in electrostatics; the green function; momentum of distributed charges. Electromagnetic waves and their propagation. Generation of electromagnetic waves, Hertz’ experience, qualitative and quantitative transport of electromagnetic waves. Electric and magnetic fields in matter: vector fields E, B, H, D, P and M. Retarded potential. Electrodynamics in relativistic notation. Lorentz transformation for electromagnetic field. Energy and momentum fields. The electromagnetic mass. The dynamics of relativistic particles and fields and the radiation of moving charges once more. Energy transport and the vector electromagnetic energy transport (Poynting Vector).

PART II: SPECIAL RELATIVITY -- Taught already by Prof. GAZEAU

Given the transformation properties of Maxwell’s equations one introduces the concept of Lorentz transformations in general and shows that they preserve the Minkowski metric. Consequences of this are elaborated including: simultaneity of events, length contraction, time dilatation, composition of velocity, transformation of acceleration. These are corroborated by the experiments of Fizeau and Michelson-Morley.

Relativistic properties of particles including the differences between rest mass and relativistic mass are explained, transformations of energy and momentum are given, and relativistic equations of motion the relativistic expression of energy, particle with zero proper mass and conservation laws of energy and momentum are discussed.