Phys356.3

Electricity and Magnetism II Prof. Alexander Moewes

 Outline Information Introduction: - Outline and objective of the course. - Overview on the key concepts. 1. Elements of vector analysis (brief refresher) Vector algebra: - Scalars and vectors: Component form, position, distance, transformation, addition, subtraction, multiplication, and triple product of vectors. Coordinate systems: - Cartesian, circular, spherical, cylindrical coordinates. Differential calculus: - Gradient, divergence and Gauss's theorem, curl and Stokes's theorem. Product rules. Integral calculus: - Line, surface and volume integrals. Scalar and Vector fields: - Classification and Helmholtz theorem. 2. Electrostatic fields in vacuum Electric field: - Electric charge, Coulomb's law, field of continuous charge distributions. - Field lines, flux density. - Gauss's law and applications. - Divergence and curl of the electric field. Electric potential: - Poisson's equation, Laplace's equation - Relation to Coulomb and Gauss's laws. Principle of the linear superposition. electric dipole. - Equipotential lines, boundary conditions. Work and Energy: - Energy density of point charge and continuous charge distribution in static fields. Conductors: - Basics, induced charges and surface charges, conductors, and capacitors.   3. Special Techniques: Laplace equation in one, two and three dimensions. Boundary Conditions and Uniqueness theorem. The method of images. Separation of variables. 4. Electrostatic fields in matter Polarization: - Convection and conduction currents. - Dielectric constant, linear, isotropic, and homogenous dielectrics. Linear dielectrics: - Susceptibility, permittivity and dielectric constant. - Boundary conditions at interfaces. - Polarization charges in materials. - Polarization and electric displacement vectors. 5. Magnetostatic fields in vacuum Lorentz Force: - Magnetic field, magnetic force, (bound) current. Bio-Savart law: - Steady currents and their magnetic fields. Divergence and curl of the magnetic field B: - Ampere's law. Magnetic vector potential: 6. Magnetostatic fields in matter, magnetic forces and magnetic materials: Magnetization: - Torques and forces on magnetic Dipoles. - Magnetization in Materials and Classification: Dia-, Para-, and Ferromagnetism. - Bound currents and magnetic field inside matter. Auxiliary field H: - Ampere's law in magnetized materials, magnetic flux density. - Magnetostatic boundary conditions. - Magnetic susceptibility and permeability. 7. Electrodynamics: General: - Ohm's Law. - Electromotive force. Electromagnetic induction: - Faraday's law. - Induction and Induction devices: transformers, generators and motors. Full system of Maxwell's equations in vacuum and matter: differential and integral form. 8. Electrodynamics and Relativity Special Relativity: - Einstein’s postulates - Lorentz transformations Relativistic Electrodynamics : - Magnetism as a relativistic phenomenon - relativistic potentials