Foundations of Classical Electrodynamics

ABOUT THE COURSE:The course offers a profound understanding of classical electrodynamics where all the problems are solved with mathematical rigor. This self-contained course begins with useful mathematical preliminaries where the students will learn from scratch the mathematical techniques used in electrodynamics. The concepts and physics of electro and magnetostatic are developed gradually with appropriate examples and mathematical problems. Finally the students will learn the development and consequences of Maxwell’s equations that govern the laws of electrodynamics.INTENDED AUDIENCE:B.Sc. , B.TechPREREQUISITES:Basic Mathematics, Vector algebra

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