Introduction to Electromagnetism

INTENDED AUDIENCE: 1st & 2nd year B. Tech. in Civil, Mechanical, Aerospace and B.Sc. Students.

COURSE PLAN: This course introduces students to handling electromagnetic theory using vector calculus. This enables students to handle problems that are more complicated than they are used to from their school days. Due to general nature of the mathematics they learn in this course, what they learn here will help them in their future courses like fluid dynamics that use similar mathematics.

Coloumb's Law.
Coloumb's Force due to several Point charges.
Force due to distribution of Charges.
What is an Electric Field?.
Electric Field due to a Charged Distribution.
Helmholtz's Theorem for Electric Field.
Divergence of a Field.
Divergence of Electric Field & Gauss's Law.
Curl Of a Field-I.
Curl of a Field-II & Stokes' Theorem.
Line, Surface Area and Volume elements in Cartesian and Cylindrical Coordinates.
Line, surface area and Volume element in Spherical Polar Coordinates.
Applications of Divergence and Stokes theorem.
Electrostatic potential.
Electric field as a gradient of potential.
Laplace's and Poisson's Equation for Electrostatic Potential.
Electrostatic Potential due to charge distribution-I Line Charge of finite length.
Electrostatic Potential due to charge distribution-II , Ring and spherical shell of charge.
Uniqueness of solution of Laplace's and Poisson's equations.
Method of Images-I, Point charge in-front of grounded metallic plane.
Method of images I; point charge in front of a grounded metallic plane and grounded metal sphere.
Laplace’s equation in some other physical phenomena.
Energy of a charge distribution - I.
Energy of a charge distribution II – an example.
Energy of a charge distribution III – energy density in terms of electric field.
Electric field and potential in a conductor.
Reciprocity theorem for conductors I.
Reciprocity theorem for conductors II – an example.
Electric polarization and bound charges I.
Electric polarization and bound charges II.
Electric Displacement.
Electrostatics in presence of dielectric materials - I.
Electrostatics in presence of dielectric materials - II.
Introduction to Magnetostatics; the Bio-Savart law.
Divergence and curl of magnetic field.
Ampere’s law for magnetic fields.
Vector potential for magnetic fields.
Calculation of vector potential for a given magnetic field.
Equation for the vector potential in terms of current density.
Vector potential from current densities - I.
Vector potential from current densities - II.
Magnetic materials I.
Magnetic materials II – bound currents and densities.
The auxiliary field -.
Solving for magnetic field of a magnet I.
Solving for magnetic field of a magnet in presence of magnetic materials.
Faraday’s law.
Induced electric field due to changing magnetic field.
Lecture 49.
Energy stored in a magnetic field - I.
Energy stored in a magnetic field II.
Displacement current.
Quasistatic approximation.
Energy transport by electromagnetic field -.
The Poynting vector.
Linear momentum and angular momentum.
Waves and wave equation.
Electromagnetic waves in free space I.
Electromagnetic waves in free space II.
Energy, intensity and momentum carried by electromagnetic waves.