Theoretical physics II WM-FI-451

1. Mathematical introduction, vectors, scalar and vector products, vector fields, gradient, divergence, curl, curves, surface and volume integrals, unoriented and oriented integrals, surface parameterization, Stokes' and Gauss' theorems, Dirac delta function in one and many dimensions.
2. Maxwel'sl equations in integral and differential form: Gauss' law for electricity and magnetism, Amper's law, Faraday's law of induction, the principle of charge conservation.
3. Electrostatics, superposition principle, electrostatic potential, Poisson's equation.
4. Multipolar expansion, charges in the electrostatic field, energy of an electrostatic system , multipolar interactions, electrostatic field energy.
5. Solving electrostatic problems, Laplace's equation in one, two and three dimensions, boundary conditions, method of images.
6. Electrostatic field in dielectrics, polarization, Gauss' law, forces acting on dielectrics.
7. Magnetostatics, Lorentz' force, Biot-Savart's law, vector potential, magnetic field energy.
8. Magnetic field in matter, magnetization: dia-, para- and ferromagnetics, magnetic moment, magnetic field energy, magnetic dipole.
9. Non-relativistic motion of charge in static fields, magnetic dipole in a magnetic field.
10. General description of the electromagnetic field, energy, Poynting's vector, potentials, Lorentz' and Coulomb's gauges.
11. Electromagnetic waves, reflection, refraction and polarization, Fresnel's formulas, waves in matter, absorption and dispersion, waveguides.
12. Green's functions for wave equation, retarded potentials.
12.Radiation of a charge, Lienard-Wichert's potentials, dipole radiation.
14. Lorentz' transformations for electromagnetic fields and potentials, four-dimensional description of fields, Lagrangian for electromagnetic field, Maxwell's equation in a four-vector language.
15. Relativistic dynamics of particles in electromagnetic fields.