The Course

In fall 2016, as part of my UofT M.Eng (course based engineering master’s), I took Electromagnetic Theory (ECE1228H), taught by Prof. M. Mojahedi.  My notes for that class (redacted: 187 pages, full version 258 pages) are available in the following forms:

The redacted version publicly available omits various assigned problems.  Feel free to contact me for the full version if you are not taking the course (and don’t intend to.)

The official course description at the time was:

Fundamentals: Maxwell’s equations, constitutive relations and boundary conditions, wave polarization. Field representations: potentials, Green’s functions and integral equations. Theorems and concepts: duality, uniqueness, images, equivalence, reciprocity and Babinet’s principles. Plane, cylindrical and spherical waves and waveguides. radiation and scattering.

New material (for me) in this course was limited to:

  • dispersion relations.
  • Druid-Lorentz model
  • quadropole moments
  • magnetic moments, magnetostatic force, and torque (mentioned in class without details, but studied from Jackson)
  • matrix representation of transmission and reflection through multiple interfaces

Mathematica notebooks associated with this course are also available.

Review of this course.

This course, despite being offered as a grad course, turned out to be largely an introductory course, which I found disappointing. I’d seen fundamentals in the course description, but assumed that this would be a more in depth attack on those fundamentals. In particular, I mistakenly assumed this would be on par with phy1510, the grad physics electromagnetism course, which also covers fundamentals, and is known as one of the most difficult grad physics courses.

I did not think that this course was taught badly.  However, I felt that spending that much time on review had no place in a graduate electrical engineering (electromagnetism) program.  Professor Mojahedi says that he has been working on expanding the scope of the course considerably, so by now, this course may be considerably different than it was when I took it.


Should you wish to actively contribute typo fixes (or additions, editing, …) to these notes, you can do so by contacting me with suggested changes, or by forking your own copy of the associated git repositories and building the book pdf from source, and submitting a subsequent merge request.

git clone peeterjoot
cd peeterjoot
submods="figures/ece1228-electromagnetic-theory mathematica ece1228-electromagnetic-theory latex"
for i in $submods ; do
   git submodule update --init $i
   (cd $i && git checkout master)

export PATH=`pwd`/latex/bin:$PATH
cd ece1228-electromagnetic-theory

I reserve the right to impose dictatorial control over any editing and content decisions, and may not accept merge requests as-is, or at all. That said, I’ll probably not refuse reasonable suggestions or merge requests.


    • Copyright
    • Document Version
    • Dedication
    • Preface
    • Contents
    • List of Figures
    • 1 Introduction.
    • 1.1 Conventions for Maxwell’s equations.
    • 1.2 Units.
    • 2 Boundaries.
    • 2.1 Integral forms.
    • 2.2 Constitutive relations.
    • 2.3 Polarization and magnetization.
    • 2.4 Linear and angular momentum in light.
    • 2.5 Helmholtz’s theorem.
    • 2.6 Problems.
    • 3 Electrostatics and dipoles.
    • 3.1 Polarization and Magnetization.
    • 3.2 Point charge.
    • 3.3 Electric field of a dipole.
    • 3.4 Bound (polarized) surface and volume charge densities.
    • 3.5 Problems.
    • 4 Magnetic moment.
    • 4.1 Magnetic moment.
    • 4.2 Conductivity.
    • 4.3 Problems.
    • 5 Boundary value conditions.
    • 5.1 Boundary conditions.
    • 5.2 Conducting media.
    • 5.3 Boundary conditions with zero magnetic fields in a conductor.
    • 5.4 Problems.
    • 6 Poynting vector.
    • 6.1 Problems.
    • 7 Time harmonic fields.
    • 7.1 Problems.
    • 8 Lorentz-Lorenz dispersion.
    • 8.1 Lorentz-Lorenz Dispersion.
    • 8.2 Calculating the permittivity and susceptibility.
    • 8.3 No damping.
    • 8.4 Multiple resonances.
    • 8.5 Problems.
    • 9 Druid model.
    • 9.1 Druid model.
    • 9.2 Conductivity
    • 9.3 Problems.
    • 10 Wave equation.
    • 10.1 Wave equation.
    • 10.2 Time harmonic form.
    • 10.3 Tunnelling.
    • 10.4 Cylindrical coordinates.
    • 10.5 Waves.
    • 10.6 Problems.
    • 11 Quadrupole expansion.
    • 11.1 Explicit moment and quadrupole expansion.
    • 11.2 Problems.
    • 12 Fresnel relations.
    • 12.1 Single interface TE mode.
    • 12.2 Single interface TM mode.
    • 12.3 Normal transmission and reflection through two interfaces.
    • 12.4 Total internal reflection.
    • 12.5 Brewster’s angle.
    • 12.6 Problems.
  • 13 Gauge freedom.
  • 13.1 Problems.
  • A Useful formulas and review.
  • B Geometric Algebra.
  • C Electrostatic self energy.
  • D Magnetostatic force and torque.
  • E Line charge field and potential.
  • F Cylindrical gradient operators.
  • G Spherical gradient operators.
  • H Spherical Laplacian.
  • I Transverse gauge.
  • J Mathematica notebooks.
  • Index
  • Bibliography


ece1228.V0.1.17-1.pdf, Sept 20, 2020 (commit df2214e1227ba2f9ffff08c31bc2dcdafc25e61f)

  • Shorten some appendix chapter headings.
  • Move some problems around.
  • Split chapter ‘Poynting vector, and time harmonic (phasor) fields.’
  • Merge wave equation chapters.
  • Fix typos in sphericalLaplacian.tex
  • Split chapter 4 into one for magnetic moments and one for boundary values.
  • convert some \paragraph to \section

ece1228.V0.1.15.pdf, Sept 15 2020 (commit a0dcf6949d054d1aa5fecd75f3747a52b2bc0980)

  • Convert to 6×9 format.
  • Remove blank lines surrounding equations.
  • Update email address.
  • Spell checking rules.
  • Don’t use dmath+aligned.
  • Fix gutter overflow issues.
  • Add periods to chapter headings.
  • Duplicate word search and fix ( ‘and and’, ‘the the’, … )
  • Spell check.
  • Fix equation grammar and overlapped equation/eq-no’s.
  • Add periods to section, paragraph, figure, problem captions.