Electromagnetic Theory

Prerequisites: PHYS W3008 or its equivalent. Fundamentals of electromagnetism from an advanced perspective with emphasis on electromagnetic fields in vaccum with no bounding surfaces present. A thorough understanding of Maxwells equations and their application to a wide variety of phenomena. Maxwells equations (in vacuum) and the Lorentz force law - noncovariant form. Scalar and vector potentials, gauge transformations. Generalized functions (delta functions and their derivatives), point changes. Fourier transforms, longitutdinal ad transverse vector fields. Solution of Maxwells equations in unbounded space for electrostatics and magnetostatics with given charge and current sources. Special relativity, Loretnz transformations, 4-momentum, relativistic reactions. Index mechanics of Cartesian tensor notation. Covariatn formulation of Maxwells equations and the Lorentz force law, Lorentz transformation properties of E and B. Lagrangian density for the electromagnetic field, Langrangian density for the Proca field. Symmetries and conservation laws, Noethers theorem. Field conservation laws (energy, linear momentum, angular momentum, stress tensor). Monochromatic plane wave solutions of the time-dependent source-free Maxwell equations, elliptical polarization, partially-polarized electromagnetgic waves, Stokes parameters. Solution of the time-dependent Maxwell equations in unbounded space with given chare and current sources (retarded and advanced solutions). Properties of electromagnetic fields in the radiaion zone, angular distribution of radiated power, frequency distribution of radiated energy, radiation form periodic and non-periodic motions. Radiation from antennas and antenna arrays. Lienard-Wiechert fields, the relativistic form of the Larmor radiation forumla, synchrotron radiation, bremsstrahlung, undulator and wiggler radiation. Electric dipole and magnetic dipole radiation. Scattering of electromagnetic radiation, the differential scattering cross-section, low-energy and high-energy approximations, scattering from a random or periodic array of scatterers. Radiation reaction force, Feynman-Wheeler theoryy. The macroscopic Maxwell equations (spatial averaging to get P, M, D, H). Convolutions, linear materials (permittivity, permeability, and conductivity), causality, analytics continuation, Kramers-Kronig relations. Propagation of monochromatic plane waves in isotropic and non-isotropic linear materials, ordinary ad extraordinary waves. Cherenkov radiation, transition radiation.