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SYLLABUS FOR PHYSICS 604
PREREQUISITES: Note that usually you must have graduate status to formally enroll
in this course. It is an official rule that an undergraduate cannot enroll in a 600-level
course unless the student has a sufficiently high gpa. It is also assumed that you have
had an upper division, (junior or senior) year long, course in electromagnetic theory.
TEXT AND REFERENCES: Classical Electrodynamics, by Jackson, third edition,
John Wiley & Sons, is the official text. Jackson uses SI units for the first 10
chapters and Gaussian units for the rest of the book. Note, however, several
additional references are available in the library.
(1)Field and Wave Dynamics, by Johnson. This text is designed for
electrical engineers and it does an excellent job of reviewing
all of electromagnetism in the first chapter. In addition it covers
waveguides in some detail. It uses only SI units, (available in college
library).
(2)Classical Electrodynamics, by Schwinger, DeRaad, Milton, and Tsai. This is a
recent graduate level text (1998) that has received excellent reviews. Julian
Schwinger received the Nobel Prize for his contributions to the theory of
electrodynamics. The text employs only Gaussian units.
(3)Electricity & Magnetism, Vol. 2, by Purcell. This is a junior-level
undergraduate text used at Berkeley. If you feel that you could use a review at the
undergraduate level this text should give it to you. It also uses Gaussian units. Note
also that Vol. II of the Feynman series is another outstanding book on
electromagnetism at the advanced undergraduate level. Still another recent text on
undergraduate electromagnetism is Introduction to Electrodynamics, (1999) by
David Griffiths. The book uses SI units.
(4)Classical Electromagnetism, by Jerrold Franklin.(2005)
This is a recent graduate physics textbook on electromagnetism. It attempts to
include the extension of electromagnetism to modern quantum field theory. It
employs Gaussian units, and the author argues strongly for gaussian units in the
preface. The text sometimes gives better explanations than Jackson does. It closely
parallels Jackson in the earlier chapters.
(5)Since as a graduate student I learned electromagnetism from Panofsky's book and
since I have previously used Panofsky's book in teaching this course, this book no
doubt influences the way I think about many of the concepts in the subject. The
book's title is Classical Electricity & Magnetism, by Panofsky &
Phillips. It employs SI units (available in the college library). This book is now also
available from Dover.
(6)Some physicists feel strongly that the quantum origins of electromagnetism are
presented better in teaching electromagnetism if the emphasis is placed on the
Vector and Scalar Potentials, rather than on Maxwell Equations using the E and Bfields. A recent book that follows this reasoning is Collective Electrodynamics, by
Carver Mead, (MIT PRESS, 2001). I intend to introduce you to concepts like the
Aharanov-Bohm Effect that emphasize these potentials if time permits.
TENTATIVE COURSE DESCRIPTION: If we were to take up every subject as it
occurs in sequence in Jackson, starting from Chapter 1 we would in one semester
not get beyond Chapter 4 and the first 4 chapters cover only electrostatics and
magnetostatics. I feel strongly that the most applied part of electromagnetism is the
part dealing with time dependent fields. For this reason whenever it is possible I am
going to digress to include material from later chapters, particularly chapters 6, 7,
and 8 which are devoted partly to propagation of electromagnetic waves. For
example, if time permits, we will investigate boundary conditions for time dependent
fields and guided waves in conductors and dielectrics. Even so, much of the useful
time dependent phenomena would have to be postponed to a second semester. An
extremely interesting chapter has been added by Jackson in his 2nd & 3rd editions,
namely Chapter I at the beginning of the book. The subjects he considers in this
chapter are timely and I hope to discuss several of them as we go along, if time
permits. I also will try to refer to applications of electrodynamics in other fields like
geophysics and optics if time permits. Finally, whenever relevant, I'll try to compare
the modern photon picture of quantum electrodynamics with the classical field
picture. This is done by Jackson in Chapter I. A book authored by Feynman and
titled QED, also introduces some of the modern concepts related to the photon. I’ll
emphasize once more that we are not going to follow the order in which topics are
covered in the text. We will start by reviewing thoroughly Maxwell Equations, and
start in the Appendix where Maxwell Equations are expressed in a general system of
units. I’ll warn you that I have overcome for myself the trauma of units in E&M by
developing Maxwell Equations in a general system of units. I am going to present
them to you. The most recent text on E&M states that the SI units will not survive
(see Franklin’s comments in his book) and remember Jackson suddenly switches
units after Chapter 10. Jackson also apologizes in his preface for using SI units at
all.
PROBLEM SHEETS: An assignment will be made in each chapter we discuss. I
really expect you to work these problems and hand them in, and to provide a little
motivation they will be counted in the final grade. There is not enough time for me to
carefully grade your problems and get them back to you in a very short period of
time. I apologize for this, but please don't make the mistake of letting the problems
ride until the night before an exam or the final due date. The problems in this text
are generally too difficult for you to employ this much-practiced technique. I'll
assume that by now you have sufficient intellectual curiosity and/or mental discipline
to budget your time for working the problems as assigned. I will grade them during
assigned grading time at the end of finals and before the deadline for grades. As
most of you know many of the problems in Jackson are worked out on the internet by
other grad students, and by previous semesters of grad students at SDSU. I feel
strongly that the best experience physics can give you is the experience of learning
how to approach and solve difficult problems on your own or with the smallest
amount of outside help possible. You will never get this experience by copying
another person’s solutions. The problems will be due within a
few days after the final exam. I will give you a final due date near the end of the
semester. If there are chapters listed below that we never get to in class then I will
announce near the end of the semester the problems you are excused from doing.
Note again that since I will not call for the problems to be handed in every week or
so, it is essential that you discipline yourself to work them as we go along. Check
with me during office hours (see below) if you have questions on the problems. The
problems in chapter 3 are especially time consuming, and often they are very hard to
work, so remember to set aside sufficient time for working on these problems. Many
of the problems in Chapter 3 involve Separation of Variables in different coordinate
systems, and I will have to assume you have learned about this technique earlier
since due to time limits I can do no more than just briefly review the technique.
STUDY OUTLINES: Study outlines like this one will be passed out to you
periodically. There will be about 28 study outlines. I am forced by a physical
limitation to present the lectures on a computer tablet. The lectures may suffer from
readability and if so I will correct and reproduce them at the next meeting. In
addition, neurological damage from surgery has caused me to close my eyes when I
am trying to concentrate on a concept. I welcome questions but you must speak loud
enough for me to hear you. The study outlines will indicate briefly the important
ideas which are discussed in lecture and warn you of digressions. In addition they
should serve as an indication of those sections in the text which will be emphasized
and those which will be omitted. When exams are made up these outlines, together
with study questions and lectures to be passed out to you, should serve as a basis for
the examination material. Finally, the problem assignments as well as answers and
hints to the problems assigned will be given in the study outlines. Some of the
problem assignments will be directly from problems included in the text and a
complete list of the problems assigned from the text occurs below. The Study
Outlines will also include problem assignments made from some of the topics
discussed in lecture.
EXAMS AND GRADING: Tentatively there will be one midterm, part in class and
part take home, and one final examination. Approximate weighting:
MIDTERM
40%(part in class, part take home, 1 week)
FINAL
45%
PROBLEMS
15%
KEEP THIS OUTLINE. IT TELLS YOU HOW THE COURSE IS TO BE GRADED.
ADDED NOTES ON LECTURES: I sincerely hope that the lectures on this subject
will not be formal. Please ask questions. So far as I'm concerned the only limitation on
questions is the fact that there is a minimum amount of subject material that we must
consider in the time allotted. On the other hand, one hour and fifteen minutes of
unbroken monologue from me could well be deadly !!
OFFICE HOURS:
P-338 or P-138
M, W, (2:30±10 -3:30PM)
T, Th available in P-338 after 2:30±10PM
F, available from 2:30±10-7:30 PM in P-338*
Sat., Sun. usually from around 3:30-8:00 PM in P-338
OFFICE PHONE: 594-6160 (I am not often near my phone, email is better)
Email: [email protected]
*Office hours will not be held if a Dept. meeting is called or a colloquium is held,
especially on Fri. afternoons at 2:00PM
.
I. Electrostatics and Properties of Fields (Jackson, Chapter 1)
A. Review of Maxwell Equations, experimental laws behind the
equations and units employed. (Note that the discussion of units in
Jackson is in the Appendix starting on page 775; part of the material below is taken
from the appendix). Jackson employs SI units in the first 10 chapters and Gaussian
units for the rest of the book. Unfortunately there are fundamental formulae used in
electromagnetism which cannot be transformed from one system of units to another
by just converting each term from one system of units to the other. One that comes
to mind is “magnetic moment”. If you started with m = IA in SI units and
converted I to Gaussian and A to CGS you would come out with the wrong answer.
For all of these reasons we are going to review Maxwell Equations and put them in a
form that is applicable to any system of units that you might encounter. For this
purpose we shall introduce 4 basic parameters that will include all unit systems,
and only 2 of them are independent. If you have trouble remembering two constants
you really need to go back and practice improving your memory skills.
1. Definitions of the electric and magnetic fields using a probe charge
Note that problems will be assigned both from the lecture material and directly from the
text with some added parts. These problems assigned from the lecture material will be
given on the study outlines. For your convenience all the problems to be assigned
directly from the text with added parts are listed below. I’ll try to list these probems also
on the study outlines when we actually discuss the subject. But sometimes I forget to
include them at the appropriate place on the study outlines SO REMEMBER THAT THE
COMPLETE ASSIGNMENT FROM THE TEXT IS THE LIST BELOW. Remember,
however, you are also expected to work the problems assigned from the lecture on the
study outlines, in addition to those assigned from the text. The problems below are from
the 3rd edition
Chapter 1: 1.1; 1.2; 1.3; 1.4; 1.5; 1.6; 1.9; 1.10; 1.12; 1.13.
Chapter 2: 2.1; 2.4; 2.7; 2.14; 2.23; 2.26.
Chapter 3: 3.1; 3.2; 3.7; 3.9; 3.14* (WITH ADDED PARTS : Treat the line charge
as system #1 and the grounded sphere as system #2. Find the self energies of the two
systems and the interaction energy between the two systems.); 3.17; 3.23.
Chapter 5: 5.1
Chapter 6: 6.17,a,b; 6.18,a,b
Chapter7: 7.2a,b; in 7.2a use both the ray and boundary value approach; 7.4a,b.
Chapter 8; 8.4a*(WITH ADDED PARTS: For both the hollow, circular cylinder and
the parallel plate guide with perfectly conducting walls solve the boundary value
problem, and find the e , h fields as well as the longitudinal fields and the cutoff
frequencies for the three cases below:)
1. TEM waves
2. TE
3. TM
The purpose of the course is to provide the student with
sufficient background and understanding in the basic concepts
associated with electromagnetic fields, Maxwell Equations, and
various types of wave propagation, including guided waves. The
expected outcome would be a better understanding of these
concepts and the ability to solve problems that arise in science
which involve these concepts. I am truly interested in conveying
to you the basic physics but at the appropriate graduate level.
You must recognize that this is not going to be a superficial
coverage of electromagnetism for someone not really interested in
the subject. I will never lecture directly from the text. I
hope I have thought about the subject enough to give you insights
not in the book. If you get hung up on one of Jackson’s
equations, see me in my office at the times listed above, but we
can’t take class time to go over individual equations in the
text.
SOME QUESTIONS I HOPE YOU WILL THINK ABOUT:
I will ask you questions related to the subjects we discuss on these outlines. The reason for the
questions is to try to get you to think about the physics behind some of the concepts introduced.
1. The expression for magnetic moment, m =IA , and the expression for the force on a charge
that moves in a magnetic field, F =qu ´ B, are correct in SI units. Are they correct in
Gaussian units? Explain.
2. In your undergraduate education in physics the subjects were broken up into categories like
mechanics, heat, light, sound, optics, wave motion and condensed matter physics. What
part of each of these subjects is completely or almost completely electromagnetism?
3. Are electromagnetic interactions still present inside the nucleus of an atom?
4. One of the concepts that you must recognize early in the study of electromagnetism if you
really want to understand it is that electric and magnetic fields are different for different
observers in relative motion with respect to (wrt) one another. Try taking some simple
examples to convince yourself of this.
5. A charge at rest wrt a given observer exhibits an electrostatic E-field. If the charge then
moves wrt the same observer will its E-field change?
6. Can divJ =0 in the vicinity of a point if the charge density is changing with time at the
point? Explain.
7. Einstein made the claim that the most fundamental equations in physics should be invariant
for all observers. Can this statement be reconciled with the fact that electric and magnetic
fields are highly dependent on the state of motion of who observes them?
8. Maxwell Equations for the E and B-fields seem to be telling us that E-fields can cause Bfields (recall Ampere’s Law) and B-fields can cause E-fields (recall Faraday’s Law) even if
there are no charges or currents anywhere. Do you believe this is true in classical
electrodynamics?
9. Will a 60 cycle electromagnetic wave travel at a different speed in vacuum than a visible
light wave? Explain .
10. Does a photon have a rest mass? Can you answer this question on the basis of classical
electrodynamics or does it require quantum field theory?
11. If the force on a probe charge is used to detect the presence of a B-field, can it detect the
presence of a B-field if it is stationary with respect to the observer?
12. If the force on a probe charge is used to detect the presence of an E-field, can it detect the
presence of an E-field if it is stationary with respect to the observer? If it is a legitimate
probe charge will the same observer detect a different E-field if it moves with respect to the
observer? Assume no change in source distributions between these two measurements.