Physics 704

Electrodynamics.

Spring 2008 -  class will meet in TH 434at 2:10 pm Tu Th

Questions and Answers

Texts: Jackson, J.D.: Classical Electrodynamics.
           Lea: Mathematics for Physicists


Learning Objectives:

After successfully completing this class, you should be able to:

Use basic principles of electromagnetism to analyze physical systems, including  systems of conductors, capacitors, wave guides, dielectrics, and current distributions.
Bring together ideas from other branches of physics, such as mechanics, when necessary to understand the behavior of a system.
Discuss the principles that apply in a given system, and clearly articulate the solution method.
Apply mathematical techniques such as separation of variables in the solution of boundary value problems in electromagnetism in rectangular, spherical and cylindrical geometries.
Use the Green's function method to solve Poisson's equation in rectangular, spherical and cylindrical geometries, and the wave equation in free space.
Use conservation principles to discuss the evolution of electromagnetic systems.
Describe the propagation of electromagnetic waves through differing media and in wave guides.
Use computer techniques to solve boundary value problems in electromagnetism.
Use computers to plot solutions to problems in electromagnetism.
Communicate your ideas clearly, orally and in writing.


Physics 704 is to cover the material in the first 8 chapters of Jackson's book; 705 covers the rest! This is a tall order, for you and for me. The objective in studying this material is not just to learn the physics of electromagnetic phenomena, but also to learn a set of mathematical techniques that are useful in many other branches of physics. In order to present the material in a way which emphasizes how a given technique can be applied in differing physical situations, and thus to avoid a good deal of duplication of material, I have attempted to construct a class schedule which does not follow the order of Jackson exactly. It is given below. We may not adhere to this schedule precisely, but it should be a guide for your reading and we can discuss how to proceed as things deviate from the plan.

Please read the appropriate section of the text before class. The material will undoubtedly be somewhat mysterious the first time you see it, and you will get more from each class if you have looked at the material in advance.

Assigned problems are listed on the schedule. Doing problems is the essence of a class based on Jackson. I shall collect and grade these every week. Do not get behind! The farther behind you get, the harder it is to catch up. Your grade for the class will be heavily based on these problem grades, although a good deal of credit will be given for a good attempt. (For what "good" means, check here.) You should include a clear and concise discussion of relevant physical principles and mathematical techniques in your solutions. Check this list for things you should NOT say in your solutions!

There will be a take-home midterm, and an in-class and a take-home final. Problems and the midterm are due at the beginning of the class period on the day indicated. Assignments turned in late will be accepted only under exceptional circumstances.  While I encourage you to discuss the problems during the semester in study groups, please be sure that the work you turn in is your own.  Exams may not be discussed with anyone except me.   You can probably find solutions to many of the problems on the internet.  These solutions range from pretty good to outright wrong.  If you can tell the difference, you don't need the solution.  If you can't, the solution won't help you.  Please review the department's plagiarism policy.   Any use of such internet resources is strictly forbidden.

Please note that some of the assignments will involve a computer calculation. You must have some familiarity with at least one computer language such as C++, FORTRAN, BASIC, IDL , or a math package such as MATHEMATICA or MAPLE. Computers may also be (and should be) used to construct plots and diagrams in other assignments.

Grades will be assigned on the following basis:
 
Homework problems:  Midterm:  Final: Project
30%  30%  35% 5%

Please feel free to discuss all aspects of the class with me at any time. Discuss the homework problems among yourselves as well as with me (exams should not be discussed, however). Try to attend published office hours, but also feel free to knock on my door whenever I am there (I'll tell you if I am busy!). It's usually a good idea to make an appointment.

As graduate students, more is expected of you. You may find it helpful, indeed necessary, to use reference materials other than Jackson. You will need a reference that discusses the basic physical principles: I recommend the Feynman lectures, and also Lea and Burke. You should have access to a mathematical reference work listing integrals as well as properties of mathematical functions such as Legendre polynomials and Bessel functions. The book store has a few copies of Gradshteyn and Ryzhik if you want your own: otherwise using the library should suffice. Other books dealing with the material include: Lea, Mathematics for Physicists, especially Chapter 8 and Optional Topic C; Landau and Lifshitz, Classical Theory of Fields; Schwinger et al, Classical Electrodynamics,  Morse and Feshbach, Methods of Theoretical Physics; Jeffreys and Jeffreys, Mathematical Physics, especially Chapters 6, 18, 21, 22 and 24. A good reference for numerical values of functions is Ambramowitz and Stegun, Handbook of Mathematical Functions (USGPO and also Dover). For numerical techniques, I recommend Numerical Recipes, Press et al.

This class will be a challenge for all of us, and I hope that we can meet it together.

Finally, check out another student's take on this class:  http://people.vanderbilt.edu/~davon.ferrara/JacksonForLife.pdf



 
Physics 704 
Course Outline
Spring 2008
Date  Jackson Reference Topic
(click on links for lecture notes)
Problems

Due date
Th Jan 24 Introduction (p1-23) Appendices  Overview: Fields and particles.  Maxwell's equations. Units. Boundary conditions
Nature of the mathematical problem. Linearity.
Tu Jan 29
6.1, 1.1-4, 5.1-3, 5.15 Derivation of Maxwell's equations from experimental results. 1.1
Jan 29
Th Jan 31
1.5-1.7, 5.4, 5.9 6.2, 6.3 , 7.1
Scalar and vector potentials. Gauge conditions.  Point charge and dipole potentials. Vector and scalar magnetic potentials.
Tu Feb 5
1.11, 5.16, 6.7 Energy in the EM field. Capacitance.
End of survey of basics.
1.2, 1.5, 5.1
Feb 5
Th Feb 7
1.8-10  
Effect of boundary conditions. Green's Theorem; uniqueness. Formal theorems
Tu Feb 12 1.12-13 Numerical methods 1.7,  5.29  Hints
Feb 12
Th Feb 14 2.1-7
Derivation of potential: method of images
Use of images to construct Green function for sphere.
Tu Feb 19 2.8-2.11
Lea Chapter 8
sections 8.1 & 2
Orthogonal functions: Sturm-Liouville problem. Separation of variables.  Rectangular 2-D and 3-D potential problems. Fourier integral.  1.17, 1.19
Feb 19
Wed Feb 20

Last day to add or drop a class
Th Feb 21
2.8-2.11
Lea Chapter 8
sections 8.1 & 2
2.12
Use of conformal transformations in 2-D problems. Polar coords in 2-D
Finite element analysis
Tu Feb 26
8.1-8.4
Boundary conditions on wave solutions: wave guides.  1.22, 1.24 Feb 26
Th Feb 28
8.4
Rectangular wave guide.
Tu Mar 4
3.1-3.4
 Lea Ch 8 Sec 8.3
Separation of variables in spherical coordinates.
2.5
Mar 4
Th Mar 6 3.5
Lea Ch 8 Sec 8.3
Separation of variables in spherical coordinates.
Spherical harmonics.
2.6
Mar 6
Tu Mar 11  3.6,  5.4-5.5
Lea Chr 8 Sec 8.3
The addition theorem
Magnetic field due to a current loop
2.26a,b; 2.27 8.5(a)  Mar 13
Th Mar 13
3.7-3.8
Lea Ch 8 Sec 8.4
Cylindrical coordinates; Bessel functions
Tu Mar 18
3.1-2 , 8.7, 3.13, 5.13 Cylindrical coordinates; Bessel functions
Examples. Mixed boundary conditions
3.3, 3.4
Start 3.16!
Mar 20
Th Mar 20  3.3-4, 5.9-12
Other problems reducible to Laplace's equation. Current flow.
Mar 24-31

SPRING BREAK, Cesar Chavez day.  Start working on P5.30
2.6 again! Apr 1
Tu Apr 1
3.9-3.10
Lea
Optional Topic C
Green's functions in terms of orthogonal functions.
 I. Spherical coordinates
Midterm handed out
Midterm due Apr 8
Th Apr 3
3.11 Green's function II: Cylindrical coordinates
Tu Apr 8 3.11
Optional Topic C
Midterm due at beginning of class
Green's function III: General method using eigenfunctions
3.16c, 5.30
Apr 15
Th Apr 10  6.4 Green's function for wave equation: causality



Class project  3.23,3.24** May 15
Tu Apr 15 4.1, 4.2 Multipole expansions 3.26, 3.27
Apr 22
Th Apr 17 4.3-4.7 Quick survey of dielectrics.
Tu Apr 22 4.3-4.7 More on dielectrics 4.1b, c and d, 6.20 Apr 29
Th Apr 24
5.6-5.7  Magnetic moment,  Force and torque 
Tu Apr 29
7.1-7.3 Force and torque  4.5, 4.7
May 6
Th May 1
7.1-7.3
Properties of waves: Polarization
Fresnel formulae


Tu May 6
7.3- 7.7 Waves in plasmas 4.8, 5.12
May 13
Th May 8 7.7-7.11 Group velocity , pulses
Tu May 13 7.7-7.11  Group velocity , pulses 7.5 May 15
Th May 15
Last day of classes.  Student reports. Class project due
Take-home final exam handed out in class

Th May 22 2:00 pm Take-home final examination due
Tu May 20
1:30 pm
In class Final Examination. 


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