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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.