Review to Coulomb?s Law, Gauss?s Law, Poisson and Laplace Equation, Greens Theorem, Electrostatic Potential Energy. Maxwell?s Equations in vacuum and in Media, Boundary Conditions at interfaces between two different media.
Solving Boundary-Value Problems: Method of Images, Green Function, Separation of variables. Laplace Equations in Spherical Coordinates, Associated Legendre and The Spherical Harmonics, Laplace Equation in Cylindrical Coordinates, Bessel Functions, Boundary-Value problem in Cylindrical Coordinates, Expansion of Green Functions in Spherical and Cylindrical Coordinates. Multipole Expansion, Boundary-Value Problem with Dielectrics, Molecular Polarizability, Electrostatic energy in Dielectric Media. Biot-Savart Law, Ampere?s Law, Vector Potential, Magnetic Moment, Force and Torque, Boundary-Value Problems. Maxwell Equations and Time varying Fields: Faraday?s Law, Energy in Magnetic Field, Maxwell Equations, Vector and Scalar Potentials, Gauge Transformations, Poynting?s Theorem, Magnetic Monopoles