PHYS 436 :: Physics Illinois :: University of Illinois at Urbana-Champaign

Physics 436 Advanced Electromagnetism II


Welcome to Physics 436!  This is the second semester of advanced electromagnetism.  We will build on the foundatin of Classical Field Theory we studied in physics 435.  We will study how EM waves propagate in dielectrics, plasmas and conductors.  We will derive fundamental Conservation Laws that identify the energy, momentum and angular momentum that EM fields possess, both in light waves as well as in static situations (hidden momentum!).  We will generalize potential theory to include time-dependence and see how gauges work when the scalar and vector potentials depend on time.  We will use potential theory to study how radiation is emitted from accelerated charges and use this to explore how nonlinear response of media leads to generation of waves at new frequencies.  We will also study propagation of EM radiation in guiding structures like hollow waveguides, optical fibers and resonant cavities.  Finally, we will very carefully study special relativity and derive a fully covariant treatment of Maxwell's equations and particle dynamics in terms of Lorentz Scalars, 4-Vectors and 4-Tensors, including radiation from relativistic charges.


Class will be held in Loomis Lab room 144 from 9 to 10 am on MWF.   Please ask questions and make comments!  That makes it better for you and your fellow students, and it makes teaching a much more enjoyable experience for me.  It's fun to talk about these topics, which are quite advanced and have many consequences and manifestations.



Grading of the course will count 2 midterm exams, the final exam, classroom participation, discussion section participation and the homework assignments.

Please review the grading scheme on the course grading page.

Academic Integrity

All activities in this course, including documentation submitted for petition for an excused absence, are subject to the Academic Integrity rules as described in Article 1, Part 4, Academic Integrity, of the Student Code.  The current plan is to have Exams carried out using the campus honor code which is spelled out in the rules noted above.

Syllabus Statements

Anti-Racism and Inclusivity Statement

The Grainger College of Engineering is committed to the creation of an anti-racist, inclusive community that welcomes diversity along a number of dimensions, including, but not limited to, race, ethnicity and national origins, gender and gender identity, sexuality, disability status, class, age, or religious beliefs. The College recognizes that we are learning together in the midst of the Black Lives Matter movement, that Black, Hispanic, and Indigenous voices and contributions have largely either been excluded from, or not recognized in, science and engineering, and that both overt racism and micro-aggressions threaten the well-being of our students and our university community.

The effectiveness of this course is dependent upon each of us to create a safe and encouraging learning environment that allows for the open exchange of ideas while also ensuring equitable opportunities and respect for all of us. Everyone is expected to help establish and maintain an environment where students, staff, and faculty can contribute without fear of personal ridicule, or intolerant or offensive language. If you witness or experience racism, discrimination, micro-aggressions, or other offensive behavior, you are encouraged to bring this to the attention of the course director if you feel comfortable. You can also report these behaviors to the Bias Assessment and Response Team (BART) ( Based on your report, BART members will follow up and reach out to students to make sure they have the support they need to be healthy and safe. If the reported behavior also violates university policy, staff in the Office for Student Conflict Resolution may respond as well and will take appropriate action.

Emergency Response Recommendations

Emergency response recommendations can be found at the following website:  I encourage you to review this website and the campus building floor plans website within the first 10 days of class.

Statements relevant to all courses offered in Fall 2021

Sexual Misconduct Reporting Obligation

The University of Illinois is committed to combating sexual misconduct. Faculty and staff members are required to report any instances of sexual misconduct to the University’s Title IX Office. In turn, an individual with the Title IX Office will provide information about rights and options, including accommodations, support services, the campus disciplinary process, and law enforcement options.

A list of the designated University employees who, as counselors, confidential advisors, and medical professionals, do not have this reporting responsibility and can maintain confidentiality, can be found here:

Other information about resources and reporting is available here:

Academic Integrity

The University of Illinois at Urbana-Champaign Student Code should also be considered as a part of this syllabus. Students should pay particular attention to Article 1, Part 4: Academic Integrity. Read the Code at the following URL:

Academic dishonesty may result in a failing grade. Every student is expected to review and abide by the Academic Integrity Policy: Ignorance is not an excuse for any academic dishonesty. It is your responsibility to read this policy to avoid any misunderstanding. Do not hesitate to ask the instructor(s) if you are ever in doubt about what constitutes plagiarism, cheating, or any other breach of academic integrity.

Religious Observances
Illinois law requires the University to reasonably accommodate its students' religious beliefs, observances, and practices in regard to admissions, class attendance, and the scheduling of examinations and work requirements. You should examine this syllabus at the beginning of the semester for potential conflicts between course deadlines and any of your religious observances. If a conflict exists, you should notify your instructor of the conflict and follow the procedure at to request appropriate accommodations. This should be done in the first two weeks of classes.

Disability-Related Accommodations
To obtain disability-related academic adjustments and/or auxiliary aids, students with disabilities must contact the course instructor and the Disability Resources and Educational Services (DRES) as soon as possible. To contact DRES, you may visit 1207 S. Oak St., Champaign, call 333-4603, e-mail or go to  If you are concerned you have a disability-related condition that is impacting your academic progress, there are academic screening appointments available that can help diagnosis a previously undiagnosed disability. You may access these by visiting the DRES website and selecting “Request an Academic Screening” at the bottom of the page.

Family Educational Rights and Privacy Act (FERPA)
Any student who has suppressed their directory information pursuant to Family Educational Rights and Privacy Act (FERPA) should self-identify to the instructor to ensure protection of the privacy of their attendance in this course. See for more information on FERPA.