Syllabus

Physics 8110 - Electromagnetic Theory II

I. Maxwell Equations, Conservation Laws 

1. Maxwell's displacement current, Maxwell's equations 
2. Vector and scalar potentials 
3. Gauge transformations, Lorentz gauge, Coulomb gauge 
4. Poynting's theorem and conservation of energy for a system of charged particles and electromagnetic
fields 
5. Conservation of linear momentum for a system of charged particles and electromagnetic fields
6. Conservation of angular momentum for a system of charged particles and electromagnetic fields

II. Plane Electromagnetic Waves and Wave Propagation 

1. Wave equations for electromagnetic waves
2. Plane waves in a non-conducting medium 
3. Linear and circular polarization
4. Reflection and refraction of electromagnetic waves at a plane interface between dielectrics. 
5. Polarization by reflection and total internal reflection 
6. Waves in a conducting medium 
7. Superposition of waves in one dimension, group velocity 

III. Wave Guides and Resonant Cavities 

1. Fields at the surface and within a conductor 
2. Cylindrical cavities and wave guides 
3. Wave guides 
4. Modes in rectangular wave guides 
5. Resonant cavities 

IV. Special Theory of Relativity 

1. The situation before 1900. Einstein's two postulates 
2. Lorentz transformations and basic kinematic results of special relativity 
3. Addition of velocities, four-velocity
4. Relativistic momentum and energy of a particle
5. Invariance of electric charge, covariance of electrodynamics
6. Transformation of electromagnetic fields

V. Simple radiating systems, Radiation by moving charges

1. Retarded potentials
2. Fields and radiation of a localized oscillating source
3. Electric dipole fields and radiation
4. Radiation from an arbitrary distribution of charges and currents
5. The Lienard-Wiechert potentials
6. The field produced by a moving charged particle
7. The field produced by a charged particle in uniform motion
8. Radiation from an accelerated charged particle at low velocities - Larmor formula.
9. Radiation from a charged particle with co-linear velocity and acceleration
10.Radiation from a charged particle confined to a circular orbit

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