## 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

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

### References

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