Faculty of Science

Objectives

To give an in-depth understanding of electric and magnetic fields using vector and integral calculus; bring out the Maxwell’s equations and derive the relativistic transformations of these fields, followed by a study of electromagnetic waves in infinite and finite media.

Contents

Introduction: The four electromagnetic equations - differential and integral forms, Laplace and Poisson equations for potential, derivation of field and potential in free space - one or two specific cases in bad conductors, good conductors, potential energy of a charge distribution, energy density in an electric field, forces on a conductor; Dielectric materials, electric polarization, electric displacement, Gauss theorem - divergence of electric field, electric field involving dielectrics - example a dielectric sphere with a point charge, Boundary conditions of potential, electric field, electric displacement at the interface between two media, method of images - one example. Magnetic induction B - Biot-Savart law (revision), forces on a moving charge in a magnetic field (revision), divergence of B, vector potential A, curl of B - Ampere's circuital law, Induced electromotive force and magnetic energy, Faraday's law- differential form, energy stored in magnetic field, Magnetization M, magnetic induction B, magnetic field intensity H, boundary conditions; Maxwell's electromagnetic wave equations: Lorentz condition, inhomogeneous wave equations for E and B, duality; Propagation of electromagnetic waves I: Free space, propagation through interface, simple wave guide, Plane waves in infinite media, free space, non-conductors, conductors;

Propagation of electromagnetic waves II: Bounded media: reflection and refraction - (a) two nonmagnetic, non-conductors (b) total reflection (c) at the surface of a good conductor,

Relativistic electric and magnetic fields of moving charges, 4-d current density vector, 4-d potential, E and B fields and Maxwell's laws for relativistic E and B.

Prerequisite: