- Outline and objective of the course.
- Overview on the key concepts.
1. Elements of vector analysis (brief refresher)
- Scalars and vectors: Component form, position, distance, transformation,
addition, subtraction, multiplication, and triple product of vectors.
- Cartesian, circular, spherical, cylindrical coordinates.
- Gradient, divergence and Gauss's theorem, curl and Stokes's
theorem. Product rules.
- Line, surface and volume integrals.
Scalar and Vector fields:
- Classification and Helmholtz theorem.
2. Electrostatic fields in vacuum
- 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.
- 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
- 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
- Convection and conduction currents.
- Dielectric constant, linear, isotropic, and homogenous dielectrics.
- Susceptibility, permittivity and dielectric constant.
- Boundary conditions at interfaces.
- Polarization charges in materials.
- Polarization and electric displacement vectors.
5. Magnetostatic fields in vacuum
- Magnetic field, magnetic force, (bound) current.
- 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:
- 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.
- Ohm's Law.
- Electromotive force.
- Faraday's law.
- Induction and Induction devices: transformers, generators and motors.
Full system of Maxwell's equations in vacuum and matter: differential and
8. Electrodynamics and Relativity
- Einstein’s postulates
- Lorentz transformations
Relativistic Electrodynamics :
- Magnetism as a relativistic phenomenon
- relativistic potentials