Overview: This course is one step ahead towards understanding some oldest phenomena of nature that mankind has ever sought after since Benjamin Franklin’s “lightning” experiment in early eighteenth century. The course begins with discussion on basic theoretical framework of electrodynamics, the Maxwell’s equations and new phenomena with respect to field theoretical questions (energy, momentum of the field) and its application to establish optics as well as in sector of practical applications (wave guides and resonant cavities) are investigated thereon.
Unit 1: Review of Maxwell’s equations, The Poynting vector, The Maxwellian stress tensor. Unit-2: Electromagnetic waves in vacuum, Polarization of plane waves, Electromagnetic waves in matter, frequency dependence of conductivity, frequency dependence of polarizability, frequency dependence of refractive index. Laws of Reflection and Refraction of Electromagnetic waves, Wave guides, boundary conditions, classification of fields in wave guides, phase velocity and group velocity, resonant cavities.
Unit-3: Moving charges in vacuum, gauge transformation, the time dependent Green function, The Lienard-Wiechert potentials, Lienard-Wiechert fields, application to fields- radiation from a charged particle, Antennas, Radiation by multipole moments, Electric dipole radiation, Complete fields of a time-dependent electric dipole, Magnetic dipole radiation.
Unit-4: Lorentz transformations, Four vectors and four tensors, The field equations and the field tensor, Maxwell’s equations for covariant notation. Relativistic covariant Lagrangian formalism, Covariant Lagrangian formalism for relativistic point charges, The energy-momentum tensor, Conservation laws.