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 which 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 exactly, but it should be a guide for your reading and we can discuss how to proceed as things deviate from the plan.

Please try to read the appropriate section of the text before class. The material will undoubtedly be 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. There will be a take-home midterm, 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.

Please note that one 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 used to construct plots and diagrams in other assignments.

Grades will be assigned on the following basis:

Homework problems: | Midterm: | Final: |

30% | 35% | 35% |

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 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: Landau and Lifshitz, Classical Theory of Fields; Morse and Feshbach, Methods of Theoretical Physics; Jeffreys and Jeffreys, Mathematical Physics, especially Chapters 6,18,21,22 and 24.

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

cheduleSPhysics 704 | Course Outline | Spring 1998 | ||
---|---|---|---|---|

Date | Jackson Reference | Topic | Problems | Due date |

W Jan 28 | I, esp.I.1,I.2; Appendix | Overview: Fields and particles Maxwell's equations. Units. | ||

F Jan 30 | I.3-6 | Nature of the mathematical problem. Linearity. Sources and boundary conditions. Fields in media: D and H. | 1.1,1.2, | Feb 4 |

M Feb 2 | 6.1,1.1-4,5.3,6.3 | Derivation of Maxwell's equations from experimental results. Boundary conditions. | ||

W Feb 4 | 6.4,6.5 | Scalar and vector potentials. Gauge conditions. | ||

F Feb 6 | 7.1, 1.5 | Kinds of solutions: static and dynamic. Plane waves. Point charge and dipole potentials. | 1.3c and d,1.5 | Feb 11 |

M Feb 9 | 5.4-5,5.9,1.6 | Vector and scalar magnetic potentials. Surface charge/current. Discontinuities | ||

W Feb 11 | 1.11,6.2,6.8 | Energy in the EM field. Capacitance. | ||

F Feb 13 | 1.8-10 | Effect of boundary conditions. Green's Theorem; uniqueness. Formal theorems | 5.1, 6.10 | Feb 18 |

M Feb 16 | President's Day holiday. | |||

W Feb 18 | 2.1-7 | Derivation of potential: method of images. | ||

F Feb 20 | Use of images to construct Green function for sphere. | |||

M Feb 23 | 2.8 | Orthogonal functions: Sturm-Liouville problem. | 1.7, 1.10, 1.14 | Feb 25 |

W Feb 25 | 2.9,2.10 | Fourier integral. Separation of variables. Rectangular 2-D potential problems. | ||

F Feb 27 | 2.11 | Use of conformal transformations in 2-D problems. | 2.1, 2.4 | Mar 4 |

M Mar 2 | 3-D problems: potential in a cube | |||

W Mar 4 | 8.1,8.2 | Boundary conditions on wave solutions: wave guides. | ||

F Mar 6 | 8.3 | More on wave guides. | 2.14, 8.4(a) | Mar 11 |

M Mar 9 | 8.4 | Rectangular wave guide. | ||

W Mar 11 | 3.1-2 | Separation of variables in spherical coordinates. | ||

F Mar 13 | 3.3-4, 5.9-12 | Examples. | 3.2, 5.7 | Mar 18 |

M Mar 16 | 3.7 | Cylindrical symmetry: Bessel functions. | ||

W Mar 18 | 3.8,8.7 | Examples | 3.11, 3.14b,c,d | Mar 25 |

F Mar 20 | ||||

M Mar 23 | 3.13,5.13 | Mixed boundary conditions | ||

W Mar 25 | Other problems reducible to Laplace's equation | |||

F Mar 27 | 3.9 | Green's functions in terms of orthogonal functions. | Midterm | Apr 1 |

M Mar 30 | 3.10 | I. Spherical | ||

W Apr 1 | Examples. | |||

F Apr 3 | 3.11 | II Cylindrical | 3.13, 5.4 | Apr 15 |

M Apr 6 - F Apr 10 | SPRING BREAK | |||

M Apr 13 | Prob 3.15 | Examples. | ||

W Apr 15 | 3.12 | General method using eigenfunctions | 3.18 | Apr 22 |

(Do not use the results of 3.15) | ||||

Class project | 3.21,3.22** | May 20 | ||

F Apr 17 | Examples. | |||

M Apr 20 | 6.6 | Green's function for wave equation: causality. | ||

W Apr 22 | 4.1, 4.2 | Multipole expansions | ||

F Apr 24 | Examples. | 3.20 | Apr 29 | |

M Apr 27 | 4.2-4.7 | Quick survey of dielectrics. | ||

W Apr 29 | Examples . | 6.19, 4.1b, c and d | May 6 | |

F May 1 | .5.6 | Magnetic moment | ||

M May 4 | 5.7 | Force and torque | ||

W May 6 | Examples | |||

F May 8 | 7.1,7.2 | Properties of waves: Polarization | ||

M May 11 | 7.3,7.4 | Fresnel formulae | 4.2 , 4.5, 4.10 | May 13 |

W May 13 | 7.5 - 9 | Dispersive media; group velocity | 5.6, 7.17 | May 20 |

F May 15 | 7.11 | Pulses | ||

M May 18 | Examples | |||

W May 20 | Student reports. Final exam handed out | |||

W May 27 | 8-10:30 am | Final Examination. (Official date) | ||

May 27 | 10.30 am | Take-home final examination due |