Foundations of Electrodynamics

Theory topics

  1. 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.
  2. 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.
  3. 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?
  4. Multipole expansion of the electrostatic potential. Derivation of the dipole approximation. The definition of the dipole moment.
  5. Electrostatic properties of matter. Polarization charges.
  6.  The boundary conditions for the electrostatic field (in the case of charged surfaces and materials with different dielectric constant). Derive!
  7. Definition of magnetic induction. Generalized Lorentz force. Biot's-Savart's law. Derive Ampere's law from it.
  8. The electromotive force in a circuit moving in an inhomogeneous magnetic field. Faraday's law of electromagnetic induction.
  9. Maxwell's equations. Maxwell's correction to the Ampère's law.
  10. Electromagnetic waves.

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