Download PY 405 – Electromagnetic Fields and Waves – Syllabus v. 1– 2010

PY 405 – Electromagnetic Fields and Waves – Syllabus v. 1– 2010
Professor Kenneth Lane
Physics 405 is the first semester of the upper-level course on electricity and magnetism. PY 355
(Methods of Theoretical Physics) is the prerequisite for this course. Of course, it is assumed that
you have passed the prerequisites for PY 355. If you do not meet these requirements, you must
consult with Professor Lane before permission to take this course can be granted.
The general plan of PY 405 is as follows: We will start in Purcell, E&M, and cover most of the
material through Chapter 9 (skipping Chap. 8). The discussion on solving Laplace’s equation will
be augmented with material from Griffiths’ book (and, possibly from Heald & Marion). The main
reason for using Purcell to acquaint you with magnetism as a relativistic phenomenon. That is the
way Purcell introduces magnetism and it is the right way to understand the appearance of magnetic
fields: they arise as a consequence of moving electric charges. We will begin this discussion with
an introduction to special relativity, sufficient to deal with the material in Purcell’s chapters 5–9.
(A good reference for this is “Mechanics”, volume 1 in the Berkeley physics series.) In Purcell, we
will learn how electric and magnetic fields transform into each other when viewed from different
inertial frames. We will also develop Maxwell’s equations (in differential form) for the electric and
magnetic fields. From these, we will be able to take a first look at electromagnetic fields and EM
waves. The topics of electric and magnetic fields in matter, solutions to the EM wave equations and
their connection with the phenomena of reflection, refraction and diffraction, and radiation will be
covered next semester in PY 406.
Instructor: Kenneth Lane, PRB 579, ext. 3-4512; [email protected]
Class: Wednesday and Friday, 3:00–4:30 PM in SCI 111..
Discussion: Thursday, 5:00–6:00 PM in PRB 148.
Office hours: Monday and Wednesday, 4:30–5:30 PM. You can usually see me at other
times by sending an e-mail or calling to make an appointment. Please take advantage of this!
Announcements will be made by e-mail. Please check your e-mail daily!
Homework Grader: To be announced. If you have a question on how to solve a homework
problem, ask me or the grader. For questions regarding grading of homework, please ask the
grader first. If you are still not satisfied, see me.
Attendance and Participation: Your attendance in class and discussion section and participation in class discussions are strongly recommended. Attendance and participation in
lecture and discussion will account for up to 10% of your course grade.
Principal Text:
Electricity and Magnetism—Berkeley Physics Course, Vol. 2, by Edward M. Purcell.
Supplemental Texts: (on reserve in the the Science Library):
Notes by K. Lane will supplement the texts and lectures.
Introduction to Electrodynamics, by David J. Griffiths
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Classical Electromagnetic Radiation, by Mark A. Heald and Jerry B. Marion.
Feynman Lectures on Physics, Vol. II, by R. P. Feynman, R. B. Leighton
and M. Sands;
Mechanics—Berkeley Physics Course, Vol. 1 by Charles Kittel, et al. This is a useful resource
on special relativity.
Final Grade: Your final grade will be based on your participation in class and discussion
sections (10%), homework (25%) two midterm exams (20% each), and the final exam (25%).
Homework assignments and their due dates appear in in the course outline below. You are
encouraged to work together on homework, but your submitted homework solutions must be
your own. The final exam date will be announced when it is available. Note: Collaboration on
exams is NEVER allowed. There will be NO make-up exams without an adequate doctor’s
(or other) excuse.
It is your responsibility to know and understand the provisions of the CAS Academic Conduct
Code. Printed copies are available in room CAS 105. I will refer cases of suspected academic
misconduct to the Dean’s Office. Proven cases of cheating on a midterm or final exam will
result at least in a zero grade for that exam.
The last day to drop classes (without a ”W” grade) is 5 weeks from the start of the semester
— Thursday, October 7. The last day to withdraw (with a ”W” grade) Friday, November 5.
See http://www.bu.edu/reg/dates/idates-fall10.html.
Format of the lectures: The topics of the lectures are listed below. They follow Purcell’s
book (and, to some extent, Griffiths’ book and my notes). I strongly recommend that you read
the relevant material, at least superficially, BEFORE I lecture on it. That way, you will have
a much better understanding of my lectures, and you will be able to ask timely questions. Following my lecture, you can go back and re-read the text and work problems to solidify your
understanding. THIS IS BY FAR THE BEST ADVICE I CAN GIVE YOU FOR
SUCCEEDING IN THIS COURSE!
COURSE & LECTURE OUTLINE – DATES ARE APPROXIMATE!
Note: In the reading assignments, P=Purcell, G=Griffiths and HM=Heald & Marion. P1 means
Purcell, Chapter 1, etc. In the homework assignments, P1-5 means Purcell, Chapter 1, problem 5;
HM1-5 means Heald & Marion, Chapter 1, problem 5, etc. Each numbered item below corresponds
to one lecture (approximately).
0. Organization of PY405; the syllabus; CGS units vs. MKS (SI) units.
1. P1: Coulomb’s law; electrostatic (potential) energy; electric field, E.
2. P1: Gauss’s law and its application to calculating E
Homework set 1, due in class 9/15: P1–1,3,5,9,15,19,21,25,30,35.
3. P2: Electric potential φ; the gradient; E(r) = −∇φ(r).
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4. P2: Examples of φ and E. Energy in an electric field; dimensional analysis for electric fields
and potentials.
Homework Set 2, due in class 9/22: P2–1,4,8,10.
5. P2: Divergence of a vector field; Gauss’s law in differential form and its meaning.; Poisson’s
and Laplace’s equations.
6. P2: Curl of a vector field; ∇ × E = 0 as the defining equation of electrostatics. Stokes
theorem.
Homework set 3, due in class 9/29: P2–13,15,16,19,23,29.
7. P3 & G3: Electrostatics; E-fields around conductors; equipotentials. Uniqueness theorem for
the solution to Laplace’s eqn.
8. P3 & G3: Simple electrostatic systems; method of images with examples; systems of capacitors.
Homework set 4, due in class 10/6: P3–1,5,7,8,9.
To be continued:
9. P3 & G3: Solutions to Laplace’s equation using Fourier series and Legendre polynomials.
10. P3, G3, HM3(??): Multipole expansions.
Homework set 5, due in class 10/13: Take from Griffiths.
11. P4: Electric currents; current densities; the continuity equation; steady currents.
12. October 15 Exam 1 in class, covers Purcell chapters 1–3.
Homework set 6, due in class:
13. Lane notes: Relativity. Einstein’s postulates; Lorentz transformations.
14. Lane notes: Lorentz transformations with examples.
15. P5: Fields of moving charges: Lorentz force; Lorentz invariance of (total) electric charge;
16. P5: Electric fields in different inertial frames; field of a point charge moving with constant
velocity; field of a charge that starts and stops.
Homework set 7:
17. P5: Force on a moving charge; interaction between moving charges (in different inertial frames)
=⇒ Magnetic fields arise from moving charges!
18. P6: Magnetic field: Definition and properties; Ampère’s law; ∇ × B and ∇ · B; B = ∇ × A;
vector potential A and its Poisson eqn.
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Homework set 8:
19. P6: Biot-Savart law; calculating B-fields; change of B at a sheet of current.
20. P6: Lorentz transformation of E and B-fields.
Homework set 9:
21. P6: Lorentz transformation of E and B-fields.
22. November 19 Exam 2 in class, covers Purcell chapters 4–6. October 15 Exam 1 in
class, covers Purcell chapters 1–3.
November 24–28 Thanksgiving break, no class.
23. P7: Electromagnetic induction: Faraday’s discovery; motion of conductors through magnetic
fields.
24. P7: Faraday’s Law of induction; the displacement current.
25. P7: Maxwell’s equations; EM waves and their velocity in vacuo.
26. Review for PY 405 final exam.
Final exam, To be announced
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