Electromagnetic Theory I

Review of curvilinear coordinates and vector calculus, vector identities, divergence and curl of vector fields Vector Calculus (cont'd); line, surface and volume integrals of vector fields, Stoke's and divergence theorems, Green's identities Electrostatics: Dirac delta in curvilinear coordinates, electric field and Coulomb's law, electric flux and Gauss' law, applications of Gauss' law, differential form of Gauss' law, curl of the electrostatic field Solution of electrostatic problems: work done on a charge displaced in an electric field, electric potential calculations for different charge configurations, electric potential gradient from centre to rim on a uniformly charged disk, electrostatic energy of charge distributions, energy density Solution of Electrostatic Problems (cont'd); Laplace's and Poisson's equations, Solution of Laplace's equation by separation of variables, rectangular boxes or pipes with specified potentials on the boundaries, potential inside a cylindrical box with specified potentials on the lateral, top and bottom surfaces, spherical geometries with azimuthal symmetry: Legendre polynomials, the electric potential due to a sphere with specified potential (or charge density) on the surface Solution of Electrostatic Problems (cont'd); spherical conductor immersed in a uniform electric field: calculation of the the electric potential and field everywhere and the induced surface charge density; electric potential and charge density near a corner or edge of a conductor; Method of images: point charge close to a grounded conducting plane, point charge near a grounded conducting sphere; Multipole expansion of the electrostatic potential Multipole expansion (cont'd); monopole, dipole, quadrupole approximations at large distances, electric field of a dipole quadrupole moment calculations of various charge distributions Electric fields in matter: dielectric media; polarization; surface and volume polarization charge densities, Gauss' law in a linear dielectric, electric displacement field, electric permittivity, susceptibility and dielectric constant in polarizable media, electrostatic energy in dielectrics Boundary value problems involving dielectrics: Boundary conditions on electric and displacement field vectors across an interface, field of a uniformly (or radially) polarized sphere, a dielectric sphere placed in an otherwise uniform electric field Boundary value problems in dielectrics (cont'd): a long dielectric cylinder placed in a uniform electric field that is normal to its axis, method of images for dielectric interfaces Electric current: current density, equation of continuity, Ohm's law, conductivity, resistivity resistance calculations, charge decay in a conductive medium Introduction to magnetostatics: Lorenz force, Biot-Savart law divergence and curl of the magnetic field, magnetic vector potential; its relation to current density, Ampere's law Magnetostatics (cont'd); Multipole expansion of the vector potential, magne