PHY1510F - GRADUATE ELECTROMAGNETISM

COURSE HOMEPAGE

The table below provides useful information about the instructor and the TA.

*This is an office hour in the sense that I will make sure to be available in my office at that time. Nevertheless, it may not be convenient for some of you. So please do feel welcome to drop by at any other time, any day, until 19h. If I am in my office and not otherwise busy with other people, you will have my undivided attention. You can also schedule an appointment by email.

The phy1510f email address should be used to communicate with the instructor about all course-related matters.
Note: email links have not been activated in a (perhaps futile) attempt to deceive address-collection software.

Course Organisation

• Text and Reference Material
  

  The textbook is J.D. Jackson's Classical Electrodynamics (John Wiley; 3^rd ed.). Errata can be found here; Jackson also has posted an updated complementary list.

  Lecture notes are posted further down on this web page. They generally follow Jackson and are quite detailed over the first four chapters, but you can expect less hand-holding as we progress through later chapters. Technical steps will increasingly be left for you to fill in. Please be aware that the notes are subject to modification! The definitive version for a given lecture will be posted soon after the lecture.

  The first chapter is a small compendium of the mathematics with which you are expected to be fairly familiar at the start of term. Essentially, this consists of:

  • General notation used
  • Vectors, differential and integral vector calculus
  • Vectors in curvilinear coordinates (only spherical coordinates are treated)
  • Expansion of functions over a complete set of orthonormal functions
  • Dirac delta-function
  • Solutions of the Laplace equation in spherical coordinates
  • Solutions of the Laplace equation in cylindrical coordinates
  
  Click here to download the mathematical preamble.
  

  You can also use this section as a reference. Note that it will not be covered in the lectures. As it is available to you before the start of term, I would strongly suggest that you take the time to go through it before lectures start. You will not be asked to prove any of the expressions given in this section.

  We shall often use the identities and expressions listed inside Jackson's front and back covers. Again, you are not asked to prove them, but you might still want to test your proficiency with coordinate notation by trying a couple of them.

• Syllabus
  

  The number ordering is by chapter in Jackson. Sections in the first three chapters dealing with topics covered in the mathematical preamble are not mentioned.

  1. Electrostatics, sections 1--11: Electrostatic field and potential; Laplace and Poisson equations, and their formal Dirichlet and Neumann solutions with Green functions; electrostatic potential energy.
  2. Boundary-Value Problems I, sections 2, 6, 9--11: Relation between Green functions and the method of images, solution of the Laplace equation in rectangular and polar coordinates.
  3. Boundary-Value Problems II, sections 3, 8--11: boundary-value problems with azimuthal symmetry and in cylindrical coordinates; Green function expansions in spherical and cylindrical coordinates applied to boundary-value problems.
  4. Multipoles, Dielectrics, sections 1--7: Multipole expansions for field, potential, and energy; electrostatics in ponderable media with boundary-value problems, susceptibility, energy in dielectrics.
  5. Magnetostatics, Faraday's Law, sections 1--12, 15--18: Laws of Amp\`ere and Biot and Savart, vector potential, magnetic field of and (force, torque) on localised current distribution, magnetic energy, magnetic fields in macroscopic media with some examples; Faraday's Law, quasi-static fields.
  6. Maxwell Equations, Conservation Laws, sections 1--5, 7--9: Displacement current, Maxwell's equations for potentials, gauge invariance; Green functions for the wave equation; Poynting's theorem in media with or without losses, applications to harmonic fields (impedance and admittance).
  7. Plane EM Waves and Wave Propagation, sections 1--9: Plane waves in non-conducting medium, polarisation, reflection and refraction, dispersion, propagation in the ionosphere and magnetosphere, wave superposition, group velocity.
  8. Waveguides, sections 1--5, 7-8, 10-11: waveguides, resonant cavities, optical fibers (multi-mode and single-mode).
  9. Radiating Systems, sections 1--4, 6: electric dipole and quadrupole radiation, magnetic dipole radiation.
  10. Scattering and Diffraction, sections 1, 2, 5, 9: Scattering at long wavelengths, perturbation theory (Rayleigh), scalar diffraction theory, diffraction by a circular aperture.
  11. Relativity and Electromagnetism in the Four-vector Formalism, sections 1--6, 9, 10: Postulates of Relativity, Lorentz transformations, velocity addition, relativistic four-vector formalism, Maxwell tensor and four-potential, transformation of fields.


• Assessment
  

  Evaluation will be based on the following:

  1. Four assignments, worth 40% of the course mark.

     Unless otherwise specified, assignments should be submitted at the beginning of class on the due date. Some tolerance will be exercised toward first-time "offenders" for delays smaller than one hour.

     Solutions will be made available.

     Lateness penalty: unless exceptional circumstances arise and an extension is granted to the whole class, late assignments will be accepted until the following Friday at noon, for the first two, and until the following Monday at noon for the third. A penalty of 5% of the mark earned will be levied as soon as a submission is deemed late, and will be increased by 5% for each extra 24-hour period that it is late until the final deadline, after which no paper will be accepted. The final deadline is on Monday, 12h, when assignments are due on Friday, and on Friday, 12h, when they are due on Tuesday.

     The assignments will consist, mostly but not exclusively, of problems from Jackson. You are welcome to use Maple or Mathematica as you see fit. If you do, your worksheet for the problem, signed, must be submitted with your paper.

  2. A final three-hour open-book (only Jackson) examination, worth 60% of the course mark. The last 45-60 minutes will be oral.

Assignments

Here are the assignments: