Maxwell’s equations, special relativity, covariant formulation of
electrodynamics, conservation laws, electrostatics, magnetostatics,
boundary conditions, electromagnetic induction, electromagnetic
waves, and elementary radiation theory.
Possible principal texts:
C. A.
Brau, Modern Problems in Classical
Electrodynamics, (Oxford Univ. Press, 2004).
F.
Melia, Electrodynamics,
(U. Chicago Press, Chicago, 2001).
Other texts to consider:
L. D. Landau and E. Lifschitz, The Classical
Theory of Fields (vol. 2).
L. D. Landau and E. Lifschitz, Electrodynamics
of Continuous Media (vol. 8).
J. D.
Jackson, Classical Electrodynamics,
(Wiley, New York, 1999).
F. E. Low, Classical Field Theory,
(Wiley, New York, 1997).
Prerequisites
The prerequisites are:
at least
one semester of an intermediate undergraduate electromagnetism
course at the level of David J. Griffiths's textbook; and
knowledge of
mathematical techniques at the level of PHY 301; and
knowledge of computational techniques, for example Mathematica
or Maple.
In Duke Physics, there is an
undergraduate "Electricity & Magnetism" course (PHY 182), with
the synopsis:
Electrostatic fields and potentials, boundary value problems,
magnetic induction, energy in electromagnetic fields, Maxwell's equations,
introduction to electromagnetic radiation.
Syllabus
Special
relativity: space-time, Lorentz
transformations, time dilation, length contraction, and velocity
transformation.
Cartesian tensors, four-vectors and
four-tensors, metric tensor,
four-vector calculus.
Thomas precession and spin.
Covariant
electrodynamics: Four-tensor electromagnetic field, transformation
of fields, electric and magnetic fields of a moving charge,
Lagrangian for charged particle in a vector
potential, Lagrangian density for the electromagnetic field.
gauge transformations, stress-energy tensor,
conservation laws.
Electrostatics:
multipole expansion,
boundary value problems, energetics,
solution methods - method of images; electrostatic screening;
Green function methods.
Magnetostatics:
magnetic scalar potential, energetics.
Dielectric
and magnetic materials: polarization,
boundary conditions, macroscopic form of Maxwell’s equations.
Faraday’s
law, coefficients of inductance, magnetic diffusion.
Electromagnetic
waves: plane waves in vacuum, energy and momentum transport,
polarization,
plane waves in materials of index n > 1; reflection and
refraction at oblique incidence (Fresnel equations),
frequency-dependent dielectric
function.
Electromagnetic
radiation: Lienard-Wiechert potentials and fields,
electric dipole radiation; Larmor formula.
multipole radiation; magnetic dipole and electric
quadrupole,
radiation from relativistic charges.
Special
topics might include, e.g., reflection from metallic surfaces,
surface plasma waves, Bremstrahlung, or synchrotron radiation.