Theory topics
- Gauss' law in the form of integral and differential. Show the relationship between them. Derive the Coulomb law and Poisson equation from the Gauss' law.
- Energy of a system of charges. Why there is an energy stored in a static distribution of charges? Derive a formula for the electrostatic field energy.
- Electrostatic properties of ideal conductors. What are they and where they come from? What is the method of image charges, and why is it correct?
- Multipole expansion of the electrostatic potential. Derivation of the dipole approximation. The definition of the dipole moment.
- Electrostatic properties of matter. Polarization charges.
- The boundary conditions for the electrostatic field (in the case of charged surfaces and materials with different dielectric constant). Derive!
- Definition of magnetic induction. Generalized Lorentz force. Biot's-Savart's law. Derive Ampere's law from it.
- The electromotive force in a circuit moving in an inhomogeneous magnetic field. Faraday's law of electromagnetic induction.
- Maxwell's equations. Maxwell's correction to the Ampère's law.
- Electromagnetic waves.