Syllabus
1. Maxwell equations and electromagnetic potentials. Mathematical formalism (Euclidean space, orthogonal coordinates, 1st and 2nd order vector operators)
2. Green function, introduction to the theory of distributions
3. Multipole expansion, separation of variables, eigenfunction expansion (spherical harmonics)
4. Electrostatics, electric potential, linear and surface charge densities, symmetries, solution in curvilinear coordinates, far-field limit, energy
5. Magnetostatics (magnetic dipole, Lorentz force, quasistationary approximation)
6. Electrodynamics (initial value problem, gauge fixing, moving charge)
7. Waves (plane wave, longitudinal and transverse waves, resonance, dipole radiation, applications to optics)
8. Conservation laws (energy, momentum, angular momentum)
9. Introduction to special relativity
10. Relativistic formulation of electromagnetism
11. Connection between macroscopic and microscopic quantities, linear and non-linear effects
Annotation
The course Principles of Physics IV - Electrodynamics will cover advanced concepts of mathematical solutions to the equations of physical fields with principal applications on classical electromagnetism (Maxwell equations) and special relativity both in static and time-dependent situations.