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 – function – Electrostatics: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 cylinder- 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.
Magnetostatics: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 – Faraday’s law: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 – Electromagnetic waves: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
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