Foundations of Classical Electrodynamics

Week 1: Mathematical preliminaries: Vector analysis, Scalar and vector fields, Vector identities using Levi-Civita symbols, Orthogonal coordinate systems and transformation. Week 2:Line, surface, volume integration, Differential calculus, Concept of gradient, divergence and curl and its representation in different coordinate system. Week 3:Statement and proof of vector theorems (Gauss’s and Stokes theorem), Curvilinear coordinate system, delta function, Helmholtz’s theorem (statement only), Tutorial-1 Week 4:Electrostatic in vacuum: quantization of charge, volume charge density and classical point charge, Continuity equation, Different aspects of Coulomb’s law, Gauss’s Law and its application (Numeric Problems). Week 5:Concept of potential, Poisson and Laplace equation, Green’s function, Electrostatic energy. Week 6:Multipole expansion, dipole and quadrupole (Problems), Electric field in matter: Conductor, Dielectric, Electric polarization, Boundary condition, Tutorial-2 Week 7:Uniqueness theorem, Electrostatic boundary value problem (Problems by solving Poisson and Laplace equation), Image method Week 8:Magnetostatic: Biot-Savart law, Applications (Problems), Divergence and curl of B, Ampere’s Law Week 9:Vector potential A, Concept of gauge, Multipole expansion, Magnetic dipole, Magnetization , Bound current, Tutorial-3 Week 10:Electromagnetic induction, Faraday’s Law (Problems), Mutual inductance. Week 11:Electrodynamics: Concept of wave equation, Maxwell’s equation in medium, Solution of the Maxwell’s wave equation, Pointing vector. Week 12:A complete over view of Maxwell’s equation, Scalar and vector potential, Coulomb and Lorentz gauge, Gauge invariance, Tutorial-4