Syllabus

• Coordinate system: Curvilinear coordinates, Laplacian in cylindrical and spherical coordinates,

Introduction to tensors, tensor form of gradient, divergence and curl, useful vector product relations,

Dirac delta function, fundamental theorems for gradient, divergence and curl [1.5 hrs]

• Electrostatics: Electrostatic equations, electrostatic potential, Coulomb’s law, Poisson’s equation,

potential and electric field due to a dipole, Gauss theorem and applications, Uniqueness theorem for

Laplace’s equation, method of images, point charge in front of plane surface and sphere, Boundary

value problems in two dimensional Cartesian and polar geometry, general solution and specific

examples, Boundary value problems in axisymmetric spherical geometry, Legendre polynomials,

Multipole expansion for an axisymmetric distribution of charges [6-8 hrs]

• Magnetostatics: Basic equations, vector potential, Biot-Savart law, Ampere’s law, multipole

expansion of magnetostatic fields, magnetic moment, magnetic medium [4-6 hrs]

• Electrodynamics and Electromagnetic Waves: Maxwell’s equation, charge conservation, sig-

nificance of Faraday’s law of electromagnetic induction, energy and momentum of electromagnetic

field, Electromagnetic waves in non-conducting medium, polarization, Electromagnetic waves in

conducting medium, skin depth, reflection and refraction at an interface between two media, waveg-

uides [8-10 hrs]

• Electrodynamics of moving charges: Retarded potential, Lineard-Wiechert potential, Electro-

magnetic radiation emitted by accelerated charges, Larmor’s formula, Radiation from oscillating

currents, Radiation from oscillating dipole, Rayleigh scattering, Synchrotron radiation [6-8 hrs]

• Relativity and Electrodynamics: Lorentz transformation, special relativity in four vector nota-

tion, Relativistic mechanics, velocity 4-vector and 4-momentum, Maxwell’s equations in covariant

form, Acceleration of charged particles in electromagnetic field, Lagrangian formulation of electro-

dynamics, gauge invariance, energy-momentum tensor, conservation laws [6-8 hrs]

Recommended Texts

• David J. Griffiths - Introduction to Electrodynamics.

• Arnab Rai Choudhuri - Advanced Electromagnetic Theory.

• J. D. Jackson - Classical Electrodynamics.

• W. Panofsky and M. Phillips - Classical Electricity and Magnetism.

• E. M. Purcell - Electricity and Magnetism.

• Michele Maggiore - A Modern Introduction to Classical Electrodynamics.

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