The course is a one semester first course on Electromagnetic Theory at B.Sc. level. This course would be a pre-requisite for the advanced level course at the M. Sc. Level.
The course begins with a review of vector calculus which is extensively used in the course. The course covers electrostatics, magnetostatics, electromagnetic induction and electromagnetic waves.
At the end of this course, a student is expected to be familiar with both the differential and integral forms of Maxwell’s equations.
No. of Lectures
Introduction to Vector Calculus:
Spherical and Cylindrical coordinates, gradient, divergence and curl, Laplacian operator.
Volume and line integrals, surface integrals, Divergence and Stoke’s theorem. Dirac delta
Coulomb’s law; forces and fields; Electric Field and Potential ; Principle of Superposition; idea of a conservative field.
Earnshaw’s Theorem; electric dipoles, field of a dipole, couple and force on a dipole, energy of a dipole; Electric double layers.
Gauss’s law; solutions for simple symmetry, capacitances, field near charged conductor;Conductors in Electrostatic field; Laplace and Poisson equations; uniqueness theorem.
Laplace’s equation in rectangular coordinates, separation of variables. Laplace’s equation in spherical coordinates, Legendre polynomials.
Conducting sphere in E field.Method of images; point charge near conducting sphere, line charge near conducting
Isotropic dielectrics; polarisation charges (ρb;σb) Gauss’s law; permittivity and susceptibility; properties of vectors D and E;
Boundary conditions at dielectric surfaces; relationship between E and P; thin slab in field, Energy of the electrostatic field, stress in a dielectric.
Electric current, Lorentz force, motion of charged particle in electric and magnetic field.
Force on and between current elements, definition of B and the Ampere’s law;
Gauss’s law; field, force, torque and energy; magnetic scalar potential, solid angle of a loop;
Ampere’s law, examples; introduction to magnetic vector potential. Field of a small current loop; magnetic dipole, dipole in an external magnetic field, Biot-Savart’s law.
Magnetic media; magnetization, existence of diamagnetism and paramagnetism; permeability and magnetic susceptibility; properties of B and H; boundary conditions at surfaces;
Methods of calculating B and H, magnetizable sphere in uniform field; electromagnets.
Emf, electromagnetic induction, Faraday’s law for a circuit, interpretation of Faraday’s emf; self-inductance, inductance of long solenoid, coaxial cylinders, parallel cylinders;
mutual inductance; transformers; magnetic energy density.
Equation of continuity, displacement current; Maxwell’s equations; electromagnetic waves, velocity of light; plane waves in isotropic media;
Energy density; Poynting’s theorem; radiation pressure and momentum; insulating media; plasmas and the plasma
frequency, evanescent waves.
Characteristic impedance, reflection and transmission at an angle, total internal reflection. Conducting media; skin effect. Guided waves.
Introduction to waveguides; TE modes; waveguide equation; cut-off frequency; characteristic impedance;cavity resonators; optical fibre, radiation by an accelerated particle, elements of antenna theory.
Introductory course on Electricity and Magnetism at Halliday & Resnick level.
D. J. Griffiths, “Introduction to Electrodynamics”,3rd Edition, Prentice Hall International (1999).
A. S.Mahajan and A, Rangwala, “Electricity and Magnetism”, Tata McGraw Hill (1988).
E. Purcell, “Electricity & Magnetism”, 2nd Edition, McGraw Hill (1985).
J. R. Reitz,F. J. Milford and R. W. Christie, “Foundations of Electromagnetic Theory”, Addison Wesley (2008).
W. Greiner, “Classical Electrodynamics”, Springer (1998).