Advanced Electromagnetic Theory (PHYS*4180)

Code and section: PHYS*4180*01

Term: Fall 2023


General Information

Department of Physics
College of Engineering and Physical Sciences 

PHYS*4180 (Section 01; Credit Weight 0.5) Fall 2023
Advanced Electromagnetic Theory

For Course Instructor, Class Time and Location, please check CourseLink.

Calendar Description

This course covers Maxwell’s equations, Lorentz-force law, conservation of charge, and conservation of energy (Poynting’s theorem). In addition, the course will discuss potentials, gauge transformations, wave equations, and multipole expansions as well as Green’s functions for the Poisson and wave equations. Additional topics include electrostatics and magnetostatics (including boundary-value problems), motion of charged particles in electromagnetic fields, and propagation and generation of electromagnetic waves.
Pre-requisites: PHYS*2340 or PHYS*2470.


Course Materials


“Introduction to Electrodynamics” by D.J. Griffiths (4th Ed.), will be the primary text. 


Selected contents from “Modern Electrodynamics” by A. Zangwill will be used as complementary material.  The book “Classical Electrodynamics” by J.D. Jackson describe all topics in this course very clearly and is an excellent reference. The content scope of both these references is beyond what will be covered in this course. 


Course Objectives

  • Acquire fluency in coordination-independent representations of fundamental laws in electrostatics and magnetostatics;
  • Acquire a good working knowledge of multipole expansion of potentials in electrostatics and magnetostatics; and in solving boundary-value problems;
  • Review Maxwell’s equations, acquire a working knowledge about energy conservation (Poynting’s theorem) and momentum conservation (Maxwell’s stress tensor); 
  • Acquire a working knowledge of wave zone (or radiation zone) solution of a harmonic source: Green’s function of inhomogeneous Helmholtz equation and Dipole approximation.
  • Acquire an understanding of general solutions to Maxwell’s equations in potential forms: Lienard-Wiechert potentials for a general (charge/current) source distribution.
  • Acquire a rudimentary understanding of the Lienard-Wiechert potentials for an arbitrarily moving point charge and the resulted fields; radiation power spatial distribution and radiation power spectrum (e.g. case of synchrotron radiation).
  • Acquire a working knowledge of multipole expansion of Lienard-Wiechert potential in the wave zone (or radiation zone): radiations from electric dipole, electric quadrupole, and magnetic dipole, Larmor formula; discuss application examples of these radiation situations.
  • Acquire a working knowledge of scattering of electromagnetic waves: Thomson scattering and Rayleigh scattering.



The choice of Schemes will favour students’ final score.

Assessment Scheme 1  Sheme 2
Quizzes 10% 10%
Assignments 30% 30%
Midterm Exam 30% 20%
Final Exam 30% 40%


Every Friday by 8 pm (exceptions: the first day of the semester, the Friday right before the midterm, the last Friday of the semester) a quiz questionary will be assigned on the course-link site and they are due by the next Monday’s class-time. These questions aim at encouraging a review of that week’s lecture content and they can be answered in an open-source fashion. Paperless submissions are handled in the same way as the homework assignments (see below). 


The distribution dates and due dates are listed in the proposed schedule (see below). Finished work will be submitted electronically on the course-link site and the marked assignments will be released to the same course-link location. Assignment deadlines will be enforced with a late penalty of 10% per day. Once a review session in class covering content of the assignment is commenced no submission will be accepted. 

Midterm Examination

Please check CourseLink.

Final Examination

Please check CourseLink.

Proposed Course Delivery Schedule

Actual dates may vary, and the updates will be announced on the course-link site. 

Week Contents Notes
Sept. 8 Introduction; Electrostatics  N/A
Sept. 11, 13, 15 Electrostatics; Magnetostatics Assign HW#1 Sept 15
Sept. 18, 20, 22 Magnetostatics N/A
Sept. 25, 27, 29 Boundary value problems HW#1 due: 8:30am,Wed Sept 27;
Assign HW#2 Wed Sept 27;
Tutorial #1 Sept 25 
Oct. 2, 4, 6 Maxwell’s equations; Wave equations (free space)  N/A
Oct. 11, 13 Energy conservation: Poynting’s theorem HW#2 due: 8:30am, Wed Oct 11;
Tutorial #2 Oct 13 (prior to Midterm)
Oct. 18, 20 Momentum conservation, Maxwell’s stress tensor   Midterm Oct. 16 (evening)
Oct. 23, 25, 27 Gauge and gauge transformations; Radiation generation: a pictorial development and Larmor formula via Thomson-Purcell approach; Radiation by antenna: harmonic case. Assign HW#3, Oct 27;
Optional Tutorial #3 to review Midterm.
Oct. 30, Nov 1, 3 Radiation by antennas: harmonic case; Green’s function of inhomogeneous Helmholtz equation; Dipole approximation. Radiation from a general case: Lienard-Wiechert potentials. N/A
Nov. 6, 8, 10 L-W potentials and Fields of an arbitrarily moving point charge; Example: v ⃗=constant case; HW#3 due: 8:30am, Wed Nov 8;
Assign HW#4 Wed Nov 8
Tutorial #4 Nov 8
Nov. 13, 15, 17 Spatial distribution of the radiated power by a point charge: from a “donut” (v≪c) to a “pencil” (v~c); Frequency spectrum of synchrotron radiation; Multipole expansion of general Lienard-Wiechert potentials. N/A
Nov. 20, 22, 24 Fields of the multipoles in the wave zone; Radiation decay examples. HW #4 due: 8:30am, Mon Nov 20;
Assign HW#5 Mon Nov 20
Nov. 27, 29, Dec 1 Scattering – Thomson; Rayleigh HW #5 due: 8:30am, Friday Dec 1. 


Course Policies

Getting Help

Office Hours: Tuesday 1:00 pm – 3:00 pm, (MACN 223) 

Additional office hours will be arranged during the time approaching exams, and these arrangements will be announced in class or via the course-link site. 

Per request or the need of the class, will initiate discussion areas on the Course-Link site associated with specific assignments, quizzes, exams, to discuss online in a public forum fashion. 

Collaboration versus Copying

Students are encouraged to discuss with each other during working on the problem assignments. However, the work that you submit as your assignment must not be a copy of someone else's work. Identical scripts will be given a mark of zero and plagiarism will be dealt with severely. Proper citations should be provided when books and other articles are used in your works. 

Course Assessment

The Department of Physics requires student assessment of all courses taught by the Department. These assessments provide essential feedback to faculty on their teaching by identifying both strength and possible areas of improvement. In addition, annual student assessment of teaching provides part of the information used by the Department Tenure and Promotion Committee in evaluating the faculty member’s contribution in the area of teaching. The Department’s teaching evaluation questionnaire invites student response both through numerically quantifiable data, and written student comments. In conformity with University of Guelph Faculty Policy, the Department Tenure and Promotion Committee only considers comments signed by students (choosing “I agree” in question 14). Your instructor will see all signed and unsigned comments after final grades are submitted. Written student comments may also be used in support of a nomination for internal and external teaching awards.


University Policies

Academic Consideration

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons, please advise the course instructor in writing, with your name, id#, and e-mail contact. See the Undergraduate Calendar for information on regulations and procedures for academic consideration.

Academic Misconduct

The University of Guelph is committed to upholding the highest standards of academic integrity and it is the responsibility of all members of the University community, faculty, staff, and students to be aware of what constitutes academic misconduct and to do as much as possible to prevent academic offences from occurring.

University of Guelph students have the responsibility of abiding by the University’s policy on academic misconduct regardless of their location of study; faculty, staff  and students have the responsibility of supporting an environment that discourages misconduct. Students need to remain aware that instructors have access to and the right to use electronic and other means of detection. Please note: Whether or not a student intended to commit academic misconduct is not relevant for a finding of guilt. Hurried or careless submission of assignments does not excuse students from responsibility for verifying the academic integrity of their work before submitting it. Students who are in any doubt as to whether an action on their part could be construed as an academic offence should consult with a faculty member or faculty advisor.

The Academic Misconduct Policy is detailed in the Undergraduate Calendar.


The University of Guelph is committed to creating a barrier-free environment. Providing services for students is a shared responsibility among students, faculty and administrators. This relationship is based on respect of individual rights, the dignity of the individual and the University community’s shared commitment to an open and supportive learning environment. Students requiring service or accommodation, whether due to an identified, ongoing disability or a short-term disability should contact Student Accessibility Services (SAS) as soon as possible.

Course Evaluation

The Department of Physics requires student assessment of all courses taught by the Department. These assessments provide essential feedback to faculty on their teaching by identifying both strengths and areas of improvement. In addition, student assessments provide part of the information used by the Department Tenure and Promotion Committee in evaluating the faculty member’s contributions in the area of teaching. You are therefore encouraged to take the evaluation procedures seriously, and to provide feedback about this course and its instructor.

Drop date

The last date to drop one-semester courses, without academic penalty, is 1 December 2023. For regulations and procedures for Dropping Courses, see the Undergraduate Calendar.