Course description:
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.