PHY 712: Electromagnetism

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1.  Office Hours: on zoom, by appointment

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2.  This course is an advanced course on Electromagnetism for graduate students. Electromagnetism is a foundational subject, and mastering its main concepts, techniques, and results will prove to be valuable for your research in optics, astrophysics, condensed matter physics, or engineering.

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3.  This is a 3 CR course. That means that the you should be spending on average 3 hours/week on lectures and 6-9 hours studying and solving homework problems. If you find yourself spending consistently more time than that, please come see me to discuss alternative learning strategies.

 

4.  The format of this course is in-person attendance and involved engagement with lectures, HW, and exams.

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5.  By the end of this course, you should be able to:

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• Derive basic results of (special) relativistic kinematics and dynamics.

• Find static solutions to Maxwell’s equations in cartesian, spherical and cylindrical coordinates.

• Use the multipole expansion to find approximate asymptotic solutions.

• Solve Maxwell’s equations inside simple continuum media.

• Describe the properties of wave solutions to Maxwell’s equations.

• Describe the propagation of waves within continuous media.

• Calculate the power radiated by a localized, oscillating source.

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6.  Learning electromagnetism from Jackson’s textbook has been a rite of passage for generations of physics graduate students. We will continue this tradition, and use the 3rd edition of the book Classical Electrodynamics by J.D. Jackson.  This textbook will be required reading. An excellent supplementary text is Zangwill.

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7. Here is a rough breakdown of the topics we will discuss in this course, together with an estimated timeline:

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• Experimental foundations of electrodynamics; Maxwell’s equations in vacuum (week 1).

• Global and local symmetries of Maxwell’s equations; electromagnetic potentials (week 2).

• Special relativity (week 3)

• Electrostatics; Poisson and Laplace equations; boundary conditions; conductors; methods of images (weeks 4-5)

• Solutions of Poisson and Laplace equations in cartesian, spherical and cylindrical coordinates; Legendre polynomials; spherical harmonics; Bessel functions (weeks 5-7)

• Magnetostatics (week 7)

• Multipole expansions (week 8-9)

• Maxwell’s equations in continuous media (weeks 9-11)

• Conservation of energy and momentum (week 11)

• Wave solutions (week 12-14)

• Radiation (weeks 14-15)

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8. Final grades for this course will be determined based on a variety of factors (the relative weight is in parentheses):

 

* Attendance and Participation (10%): This is a small class, and thus there will be plenty of chances to participate, e.g. by asking and answering questions. While doing so, please be mindful of classmates and allow everyone the same opportunity to contribute to the class. The participation grade will be based on the quality and not the quantity of contributions. Participation also includes helping classmates when they have questions. 10% of the grade might not seem like much, but it’s the difference between an A grade and a B grade at the end of the semester.

 

* Final Exam (20%): This will be a cumulative exam.  The exam should take only a few hours to complete. During the exam, you are allowed to consult your notes, Jackson, and past homework sets, but you cannot use other books nor (duh!) google the answers.

 

* Homework (30%): Each Monday morning I will assign a set of homework problems, which will be due the following Monday by the end of the day (unless there is a midterm that week, in which case there might be some more flexibility). I will not assign new homework sets during the weeks when midterms are scheduled to ensure that you have extra time to prepare for the exams. Homework assignments will be posted on canvas, where you will also be able to upload your solutions. You can just scan your handwritten solutions with your phone (let me know if you need suggestions about scanning apps), no need to type up your solutions (although you are welcome to do so if you prefer it). There will be a total of 12 homework assignments. At the end of the semester I will drop the lowest score. When working on your homework, you are welcome to discuss the problems with your colleagues (see however the “Academic Integrity” section for important disclaimers). You are also allowed (but not required) to use software such as Mathematica and/or Matlab to deal for instance with integrals involving special functions. Both Mathematica and Matlab are available for free to all WFU students, and come with extensive documentation. Homework problems will be challenging, so please make sure to start working on them early as late homework will not be accepted.

 

*  Interterm Exams (40%): We will have 2 interterm exams. These will be 2-hour, in-class exams. Exams are due 2 hour after the start time. During the midterms you are allowed to consult your notes, Jackson, and past homework sets but, you cannot use other books nor google the answers. At the end of the semester, all your scores will be combined in the proportions shown above to determine your final grade based on the following grading scale: A: 100-90% B: 89-80% C: 79-70% D: 69-60%.  The lowest passing grade for this class is B-

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9.  Course Policies

 

• Technology in class. For obvious reasons, technology will be an integral part of this course. However, I suggest you turn off your cellphone and computer notifications during class, and I strongly caution you against multitasking while in class. Lectures will be fast-paced, and it is likely that you will miss something important—at the very least some participation points— while checking your email or surfing the web.​

• Office Hours. Office hours are also on zoom, and by appointment only. If you would like to schedule a meeting, please send me an email including (1) the topics you would like to discuss (e.g. electric dipole radiation, Problem 2 on this week’s homework, etc...), (2) expected duration, and (3) a couple of time windows (during Mon-Fri, 9am-6pm) that work for you.

• Learning Accommodations. If you need special accommodations for this course, please contact the Center for Learning, Access, and Student Success (CLASS). Once you have obtained an accommodation letter from this office, please contact me as early as possible in the semester so that we can set up an appointment to privately discuss your needs. I will make every effort to provide you with any reasonable accommodation you may need.

• You can learn more about WFU’s official policy for student accommodation on the University website.

• Make-up Exams and Late Work. There are no make-up exams and late work will not be accepted, except in case of documented medical emergencies or particular learning accommodations.

• Re-grade policy. If you would like me to review a graded assignment (homework or exam), please submit a request by email within one week from the day it has been returned to you. Your email should state clearly the reason why you are requesting a re-grade. Exceptions to this policy may apply to the final exam due to the university deadline for submitting final grades. Please be aware that your grade could end up increasing or decreasing as a result.

• Academic Integrity. You are allowed to work in groups on the homework problems. However, the solutions you turn in for grading should be your own work and reflect your own understanding of the material. In particular, while you are welcome to consult other electromagnetism books to further your understanding of the subject, looking for solutions to homework or exam problems in other textbooks or online amounts to cheating. Copying someone else’s work, whether from a book or from a colleague, is considered plagiarism and will be sanctioned according to WFU’s policy. For more information about WFU’s policy on academic integrity, please see the student handbook.​

• Diversity, Inclusion and Harassment. This class is a safe learning environment where diversity is valued and any form of harassment will not be tolerated. Please feel free to reach out to me if you feel that these values are not being respected. However, you should be aware that the university requires me to report any serious incident that is disclosed to me, regardless of whether it took place on- or off-campus. While I am unable to promise confidentiality, I can assure you that I will handle any situation with discretion. You can also report any unethical behavior you witness on campus directly to the WFU Ethics Committee​.

• Take care of yourself. Being a Ph.D. student can be a very fulfilling but also very demanding experience. One of the most valuable skills you should aim to learn while in graduate school is the ability to deal with a heavy workload without compromising your well-being. Please make sure to take care of yourself and carve out enough time during the week to eat well, have enough sleep and do things you enjoy outside physics. In the long run, this will make you more likely to succeed here at WFU. If at any point during the semester you feel overwhelmed, please know that it is normal and make sure to reach out to people you’d feel comfortable talking with. These may include not only your friends and family, but also your fellow graduate students, your instructors, other faculty members, as well as resources on campus such as the Center for Learning, Access, and Student Success.

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PHY 787: E&M Workshop

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The meeting times of this lecture series will be announced. It is chosen so that everyone that signs up can attend so at the beginning of the semester a survey will be sent out.

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1.  Office Hours: on zoom, by appointment

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2.  This course is an advanced course on Electromagnetism for graduate students. Electromagnetism is a foundational subject, and mastering its main concepts, techniques, and results will prove to be valuable for your research in optics, astrophysics, condensed matter physics, or engineering. This "workshop" is offered in a series of lectures that aid the student in bridging the gap between the mathematically dense, mainly classical presentation of Jackson and the modern research topics of faculty within our department. It essentially replaces E&M II in the topics it covers. 

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3.  This is a 1.5 CR course. That means that the you should be spending on average 1 hour/week on the lecture and 2 hours on reading. 

 

4.  The format of this course is in-person attendance and involved engagement. There is some reading, no exams, no HW

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5.  By the end of this course, you should be able to:

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• Identify areas of Electromagnetic theory used in the basic research foci of our department

• Read and comprehend current literature in quantum circuits, exotic magnetism, nonlinear optical phenomena, scattering in turbid media, etc.

• Have a rudimentary knowledge of the transition from classical E&M to Quantum electrodynamics

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The policies of the class are the same as for PHY 712 where applicable.

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Grading is based only on attendance and participation using the scale above.

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The Schedule...