PHY1510S - GRADUATE ELECTROMAGNETISM

COURSE HOMEPAGE

2020

Lecture schedule and location:

TR13:00, F12:00

MP1115

First meeting on Tuesday, January 7, 13:00, in MP1115.

The table below provides useful information about the instructor.

* Fixed office hours may not be convenient for some of you. So do feel welcome to drop by at any time, any day, until 18h. If I am in my office and not otherwise busy with other people, you will have my undivided attention. If I am not around, leave a message with my keeper (April) in MP129, and I will get back to you. 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: The email link has not been activated in a (perhaps futile) attempt to deceive address-collection bots.

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 a list which contains extra items.

  Lecture notes are posted further down on this web page. They generally follow Jackson (with some variation in content and ordering!). Please be aware that the notes are subject to modification! Notes for each lecture will be posted soon after the lecture. The definitive version for the current year will appear as a cumulative file containing complete, hyperlinked notes covering all previous material and updated every two weeks.

  The first chapter is a mathematical preamble with which you are expected to be fairly familiar at the start of term. Much of it is taken from Jackson's chapters 2 and 3. Topics it covers are:

  • 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
  • Solution of the Laplace equation in rectangular coordinates
  • Solution of the Laplace equation in spherical 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 index 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 solutions in terms of Green functions; electrostatic potential energy.
  2. Boundary-Value Problems I, sections 2, 6: Green functions as a generalisation of the method of images.
  3. Boundary-Value Problems II, sections 3, 9--10: boundary-value problems with azimuthal symmetry; Green function expansions in spherical coordinates applied to boundary-value problems.
  4. Multipoles, Dielectrics, sections 1--7: Multipole expansions for field, potential, and energy; electrostatics in media with boundary-value problems, susceptibility, energy in dielectrics.
  5. Magnetostatics, Faraday's Law, sections 1--12, 15--18: Laws of Ampère 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's Equations, Conservation Laws, sections 1--5, 7--9, 13: Maxwell's equations for fields and potentials; Cauchy initial-value problem of the theory and gauge arbitrariness; Green functions for the wave equation; Poynting's theorem in media with applications to harmonic fields; Hertz superpotential formulation of the theory.
  7. Plane EM Waves and Wave Propagation, sections 1--6, 8-9, 11: Plane waves in non-conducting media, polarisation, reflection and refraction, application of Hertz superpotential to interaction of a wave with an interface (not in Jackson); dispersion, wave superposition, group velocity.
  8. Not covered.
  9. Radiating Systems, sections 1--4, 6: electric dipole and quadrupole radiation, magnetic dipole radiation.
  10. Not covered.
  11. Relativity and Electromagnetism in the Four-vector Formalism, sections 1--6, 9, 10: Postulates of Relativity, Lorentz transformations, relativistic four-vector formalism, Faraday field tensor, four-potential, transformation of fields.
  12. Particle and Field Dynamics: Motion of particles in electromagnetic fields and Maxwell field equations derived in Lagrangian and Hamiltonian formalism. Relativistic Dynamics and Energy-Momentum of EM Fields, sections 10-11: Energy-Momentum tensor and conservation laws, invariant Green functions for the wave equation.
  13. Not covered.
  14. Fields and Radiation from Relativistic Point-charges in Arbitrary Motion, sections 1-3: Liénard-Wiechert potentials and Lorentz form-invartiant fields; radiated power, non-relativistic and relativistic.


• Assessment
  

  Evaluation will be based on the following:

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

     Unless otherwise specified, assignments should be submitted in my office by 17:00 on the due date. Some tolerance will be exercised toward first-time "offenders" for delays not exceeding one hour.

     Lateness penalty: unless exceptional circumstances arise and an extension is granted to the whole class, late assignments will be accepted under the following terms: 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, 17h, when assignments are due on Friday, and on Friday, 17h, when they are due on Tuesday.

     The assignments will consist mostly 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. Mathematica is available on the Physics server. If you run Linux or Mac, just log into your account via ssh -X; if you run Windows, you will need to install putty, to connect to our server, and an X emulator for Windows to run Mathematica in graphic mode. Links are provided on this page by our Physics Computing Services. Make sure to use only the SSH option in putty, as telnet is not secure (it sends passwords in unencrypted...).

     A friendly word of caution about the assignments. Everyone knows how to find Jackson solutions on the web, but do not even hope that you can get a decent mark on the exam if you have not done these problems yourself. By all means discuss them with colleagues and with me if you feel stuck. Also, at U of T, plagiarising from the web is an academic offence that you definitely do not want on your record. You may wish to (re)acquaint yourself with the Code of Academic Behaviour, or visit the Academic Integrity website. Random checks will be conducted to detect plagiarism.

  2. A three-hour open-book (only Jackson) examination, worth 60% of the course mark. The exam will consist of an initial 2-hour period during which the candidate will work on a set of questions, after which we (the candidate and I) shall discuss their written work in my office for a maximum of about one hour.

Lecture Notes

A cumulative file of the current lecture notes, updated avery couple of weeks, is also available. It now contains all this year's notes, corresponding to chapters 1-7 , 9, and 11, 12 and 14 of jackson (only the sections covered in the notes!).