Course Identification

Electromagnetism course in BSc studies

1. Recapitulation of Coulomb's law, Earnshaw's theorem, Amp`ere's law, Faraday's law, the force acting on a non-relativistic charged particle moving in an electromagnetic (EM) field, charge conservation and the continuity equation, the Hall effect, the dielectric permittivity of a dielectric and of a metal, the plasma frequency. The electric permittivity and conductivity of a composite medium. The percolation phenomenon.
2. Derivation of Maxwell's equations in vacuum and in matter by generalizing the above laws and adding the displacement current.
3. Energy density and Poynting's vector, work of the EM field.
4. Simple solutions of Maxwell?s equations: Plane wave, velocity of light, phase velocity and group velocity, surface plasma waves, waves in an electrical conductor, the skin depth, Snell?s laws of refraction, negative refraction. The EM vector potential. The Aharonov-Bohm effect.
5. Radiation by a charged, non-relativistic, accelerated particle.
6. Qualitative theory of scattering of an EM wave in an inhomogeneous medium, polarization of the scattered wave.
7. Relativity theory, four-vectors, the fields E and B as components of a four-tensor, Newton's second law for a relativistic charged particle in an EM field, synchrotron radiation.
8. Magnetic monopoles and the quantization of electric charge.

Upon successful completion of this course students should be able to:

1. Demonstrate understanding how Maxwell's equations arise from generalizations of experimental observations and more specific rules for particular cases.
2. Demonstrate understanding of wave propagation in vacuum, in dielectric media, in conducting media, and along an interface between a conductor and a dielectric (surface plasma waves).
3. Understand the reflection and refraction of electromagnetic (EM) waves at an interface between two otherwise homogeneous media.
4. Understand the scattering of EM waves by inhomogeneities in the medium, including the polarization of the scattered wave.
5. Understand how the special theory of relativity arises from EM theory; EM fields as four dimensional second rank tensors.
6. Understand the treatment of EM fields in a macroscopically inhomogeneous medium.

Bibliography:

1. Classical Electrodynamics by J. D. Jackson, 2nd ed., Wiley.
2. Advanced Electromagnetism: Lecture notes for high school teachers---fifth edition by David J. Bergman