Duke Physics

Electrodynamics (PHY 311)

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:

1. C. A. Brau, Modern Problems in Classical Electrodynamics, (Oxford Univ. Press, 2004).
2. F. Melia, Electrodynamics, (U. Chicago Press, Chicago, 2001).

Other texts to consider:

1. L. D. Landau and E. Lifschitz, The Classical Theory of Fields (vol. 2).
2. L. D. Landau and E. Lifschitz, Electrodynamics of Continuous Media (vol. 8).
3. J. D. Jackson, Classical Electrodynamics, (Wiley, New York, 1999).
4. 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:

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.

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