## PHY 401: Classical Electrodynamics II

3 credits | Prerequisites: PHY 302

### Course rationale

This core course is the continuation of Classical Electrodynamics 1. Two main focuses of this course are dime-dependent electromagnetic phenomena and relativistic formulation of classical electrodynamics. Starting with the review of Maxwell’s equation this course develops wave phenomena, scattering, and radiation. Invariance of the Maxwell’s equations under a coordinate transformation called Lorentz transformation was one of the seeds of Einstein’s special theory of relativity. In the last part of this course, these topics are discussed.
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### Course content

Review of Maxwell’s Equations: Maxwell’s equation in differential and integral form, boundary value problem in electrostatic, Green’s function, Laplace’s equation in different coordinates, spherical harmonics; Properties of Electromagnetic Field: electromagnetism as a gauge theory, different gauges, Poynting theorem, conservation of energy and momentum, transformation properties of the electromagnetic field under rotation, reflection and time reversal, magnetic monopole, Dirac quantization condition; Electromagnetic Waves: wave in various dimensions, electromagnetic waves in vacuum, linear and circular polarization, Stokes parameter, reflection and refraction, magnetohydrodynamic waves, superposition of waves, phase and group velocity; Waveguides: cylindrical cavities, rectangular waveguides, modes in a rectangular waveguide, energy flow and attenuation in waveguides, power loss in a cavity, Q factor; Radiating Systems: fields and radiation of an oscillating source, electric dipole, magnetic dipole and electric quadrupole, linear antenna, spherical wave equation, multipole expansion; Scattering and Diffraction: scattering cross section, Thomson scattering, Rayleigh scattering, scalar and vectorial diffraction theory, optical theorem; Special Theory of Relativity: Einstein’s postulates, Lorentz transformation, relativistic kinematics, invariance of electric charge, covariance of electrodynamics, transformation of electromagnetic fields; Dynamics of Relativistic Particles and Fields: Lagrangian and Hamiltonian of a relativistic charged particle, motion in uniform electric and magnetic field, Proca Lagrangian, photon mass effects, solution of wave equation in covariant form; Collisions and Scattering: energy transfer for collisions in Coulomb potential, energy loss in soft collisions, density effects, Cherenkov radiation, elastic scattering; Fields from Moving Charge: Lienard-Wiechert potential, radiation in time and frequency domain, synchrotron radiation.

### Course objectives

1. Understand various advanced concepts related to electrodynamics.
2. Apply vector and tensor calculus to express the laws of electrodynamics.
3. Use appropriate mathematical formalism to solve different problems of interest.
4. Familiarize with Einstein’s special theory of relativity.
5. Understand the relativistic mechanics of electrodynamics.

### References

1. Classical Electrodynamics (3rd edition) by John David Jackson
2. Modern Electrodynamics (1st edition) by Andrew Zangwill
3. Classical Electrodynamics by Julian Schwinger, Lester L. Deraad Jr., Kimball A. Milton, Wu-yang Tsai, Joyce Norton
4. Classical Electrodynamics (2nd edition) by Hans Ohanian
5. Advanced Classical Electrodynamics: Green Functions, Regularizations, Multipole Decompositions by Ulrich D Jentschura