CLASSICAL ELECTRODYNAMICS – I

Electrostatics: Electric field; Gauss Law; Differential form of Gauss’ law; Equation of electrostatics and the scalar potential; surface distribution of charges and dipoles and discontinuities in the electric field and potential; Poisson and Laplace equations; Uniqueness Theorem; Green's Reciprocity Theorem; Formal solutions of potential by Green's function; Electrostatic potential energy and energy density.

Boundary Value Problems in Electrostatics: Methods of Images; A point charge near an infinite conducting plane; Point charge in the presence of a conducting sphere: Case (a) When the conducting sphere is grounded; Case (b) When the conducting sphere is insulated; Case (c) When the conducting sphere is charged and insulated; Conducting sphere in a uniform electric field by method of images; Green function for the grounded conducting sphere in the field of a charge q; Green function for the sphere: General solution for the potential; Conducting sphere with hemispheres at different potentials; Orthogonal functions: Expansion of arbitrary functions in terms of a complete set of functions; Examples of systems of orthonormal functions: Fourier series, Fourier Integrals.

Multipoles, Electrostatics of Macroscopic Media, Dielectrics: Spherical Harmonics; Multipole expansions; Monopole moment; Dipole moment; Quadruple moment; Multipole expansions in Cartesian coordinates; multipole expansion of the energy of a charge distribution in an external field; Elementary treatment of electrostatics with permeable media; Boundary value problems with dielectrics; Molecular polarizability and electric susceptibility; A molecular model of the polarizability; Models for molecular polarizability: Displacement polarization, Orientation Polarization; Electrostatic energy in dielectric media.

Magnetostatics: Introduction and definition; Biot-Savart Law; the differential equation of Magnetostatics and Ampere's law; Vector potential and magnetic induction for a circular current loop; magnetic fields of a localized current distribution, magnetic moment; force and torque on and energy of a localized current distribution in an external magnetic induction; macroscopic equations, boundary conditions on B and H; methods of solving Boundary value Problems in Magnetostatics; uniformly magnetized sphere; magnetized sphere in an external field, permanent magnets; magnetic shielding, spherical shell of permeable material in a uniform field.

Maxwell's equations ,conservation laws: energy in a magnetic field, vector and scalar potentials, Gauge transformations, Lorentz gauge, Coulomb gauge, Green function for the wave equation, derivation of the equations of macroscopic electromagnetism, Poynting's theorem and conservation of energy and momentum for a system of charged particles and EM fields, conservation laws for macroscopic media, electromagnetic field tensor, transformation of four potentials and four currents, tensor description of Maxwell's equations.