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.
BioSavart 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
