Phys 3630 Electro- and Magnetostatic Theory

Syllabus - 2014

1. Vector Analysis Review

• Gradient and Curl in various coordinate systems.
• Line, surface and volume integrals.
• Divergence and Stoke’s theorem.
• Helmholtz theorem.
• Laplacian operator.
• Dirac delta function.
  

2. Electrostatics

• Coulomb’s law and the electric field of a point charge.
• Electrostatic potential.
• Continuous charge distributions.
• Divergence of E and Gauss’s law.
• Laplace and Poisson equations.
• Potential energy of an arbitrary charge distribution.
• The electric dipole.
• The electrostatic multipole expansion.
• Quadrupole tensor.
• Dielectric materials - polarization vector, potential and field at an interior and exterior point.
• The displacement vector D.
• The electric susceptibility and permittivity.
• Energy density in a dielectric medium.
  

3.Magnetostatics

• Current density J and the continuity equation.
• The magnetic force law and the magnetic induction B (Biot-Savart law).
• The divergence of B and the vector potential A.
• The curl of B and Ampere’s law.
• The magnetic dipole.
• The magnetic multipole expansion.
• Magnetic energy density.
• Magnetic materials- magnetization vector, vector potential and magnetic
  induction at an interior and exterior point.
• The magnetic field intensity H .
• The magnetic susceptibility and permeability.
• Energy density in magnetic materials.
  

4. Electrodynamics

• Magnetic flux.
• Faraday’s law.
• Electric fields induced by time varying magnetic fields.
• Magnetic fields induced by time varying electric fields.
• Displacement current.
• Complete form of Ampere’s circuital law for H.
  

5. Maxwell’s Equations

• Differential form in terms of E, D , B and H .
• Differential form in terms of E and B.
• Differential form for linear, isotropic, homogeneous media.
• Integral form.
• Boundary conditions on the 4 field vectors.
• Poynting’s theorem.
• The time dependent electromagnetic potentials - wave equations for A and φ, gauge transformations.

6. Laplace’s and Poisson’s Equations

• Solutions of Laplace’s equation in rectangular, spherical and cylindrical coordinates.
• Solution of Poisson’s equation in the case of spherical symmetry