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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 

Course Objectives

 

 

 

Course Outline

 

 

 

Schedule

 

 

 

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