Electrodynamics

Course Number: PHY762

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: 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.

Sample lecture schedule #1

(based on 25 lectures each of duration 75 minutes).

  • Lecture 1: Review of undergrad EM, part 1: electrical charge, electric field and potential, current, magnetic field and vector potential, and electromagnetic energy.
  • Lecture 2: Review of undergrad EM, part 2: Faraday’s law, Maxwell’s equation in vacuum, electromagnetic waves, and Poynting’s Theorem.
  • Lecture 3: Special relativity 1: Background review - Space-time, Lorentz transformations, time dilation, length contraction, and velocity transformation.
  • Lecture 4: Special relativity 2: Review of Cartesian tensors, four-vectors and four-tensors, metric tensor.
  • Lecture 5: Special relativity 3: Four-vector calculus.
  • Lecture 6: Special relativity 4: Thomas precession and spin.
  • Lecture 7: Covariant electrodynamics 1: Four-tensor electromagnetic field, transformation of fields, electric and magnetic fields of a moving charge.
  • Lecture 8: Covariant electrodynamics 2: Lagrangian for charged particle in a vector potential, Lagrangian density for the electromagnetic field.
  • Lecture 9: Covariant electrodynamics 3: Gauge transformations, stress-energy tensor, and conservation laws.
  • Lecture 10: Electrostatics 1: Multipole expansion of the electrostatic field.
  • Lecture 11: Electrostatics 2: Boundary value problems (BVPs) – systems of conductors; coefficients of capacitance; energetics.
  • Lecture 12: Electrostatics 3: BVP solution methods - Method of images; electrostatic screening; fields near tips and edges.
  • Lecture 13: Electrostatics 4: BVP solution methods: Green function methods.
  • Lecture 14: Magnetostatics: Magnetic scalar potential, energetics.
  • Lecture 15: Dielectric and magnetic materials (phenomenological treatment): polarization, boundary conditions, macroscopic form of Maxwell’s equations.
  • Lecture 16: Faraday’s law, coefficients of inductance, magnetic diffusion.
  • Lecture 17: Electromagnetic waves 1: plane waves in vacuum, energy and momentum transport, polarization.
  • Lecture 18: Electromagnetic waves 2: plane waves in materials of index n > 1; reflection and refraction at oblique incidence – Fresnel equations.
  • Lecture 19: Electromagnetic waves 3: elementary theory of frequency-dependent dielectric function.
  • Lecture 20: Electromagnetic radiation 1: Lienard-Wiechert potentials and fields.
  • Lecture 21: Electromagnetic radiation 2: Electric dipole radiation; Larmour formula.
  • Lecture 22: Electromagnetic radiation 3: Multipole radiation; magnetic dipole and electric quadrupole.
  • Lecture 23: Electromagnetic radiation 4: Radiation from relativistic charges.
  • Lecture 24: Special topics.
  • Lecture 25: Special topics.

Special topics might include, e.g., reflection from metallic surfaces, surface plasma waves, Bremstrahlung, or synchrotron radiation.

Sample lecture schedule #2

(based on 25 lectures each of duration 75 minutes).

  • Lecture 1: Review of undergrad EM, part 1: electrical charge, electric field and potential, current, magnetic field and vector potential, and electromagnetic energy.
  • Lecture 2: Review of undergrad EM, part 2: Faraday’s law, Maxwell’s equation in vacuum, electromagnetic waves, and Poynting’s Theorem.
  • Lecture 3: Electrostatics 1: Multipole expansion of the electrostatic field.
  • Lecture 4: Electrostatics 2: Boundary value problems (BVPs) – systems of conductors; coefficients of capacitance; energetics.
  • Lecture 5: Electrostatics 3: BVP solution methods - Method of images; electrostatic screening; fields near tips and edges.
  • Lecture 6: Electrostatics 4: BVP solution methods: Green function methods.
  • Lecture 7: Magnetostatics: Magnetic scalar potential, energetics.
  • Lecture 8: Dielectric and magnetic materials (phenomenological treatment): polarization, boundary conditions, macroscopic form of Maxwell’s equations.
  • Lecture 9: Faraday’s law, coefficients of inductance, magnetic diffusion.
  • Lecture 10: Electromagnetic waves 1: plane waves in vacuum, energy and momentum transport, polarization.
  • Lecture 11: Electromagnetic waves 2: plane waves in materials of index n > 1; reflection and refraction at oblique incidence – Fresnel equations.
  • Lecture 12: Electromagnetic waves 3: elementary theory of frequency-dependent dielectric function.
  • Lecture 13: Special relativity 1: Background review - Space-time, Lorentz transformations, time dilation, length contraction, and velocity transformation.
  • Lecture 14: Special relativity 2: Review of Cartesian tensors, four-vectors and four-tensors, metric tensor.
  • Lecture 15: Special relativity 3: Four-vector calculus.
  • Lecture 16: Special relativity 4: Thomas precession and spin.
  • Lecture 17: Covariant electrodynamics 1: Four-tensor electromagnetic field, transformation of fields, electric and magnetic fields of a moving charge.
  • Lecture 18: Covariant electrodynamics 2: Lagrangian for charged particle in a vector potential, Lagrangian density for the electromagnetic field.
  • Lecture 19: Covariant electrodynamics 3: Gauge transformations, stress-energy tensor, and conservation laws.
  • Lecture 20: Electromagnetic radiation 1: Lienard-Wiechert potentials and fields.
  • Lecture 21: Electromagnetic radiation 2: Electric dipole radiation; Larmour formula.
  • Lecture 22: Electromagnetic radiation 3: Multipole radiation, magnetic dipole and electric quadrupole.
  • Lecture 23: Electromagnetic radiation 4: Radiation from relativistic charges.
  • Lecture 24: Special topics
  • Lecture 25: Special topics