PHYSICS 405

Schedule for the Chapters
1. Ch. 1: Vector Analysis and Curvilinear Coordinates: 18-30 January (first 2 weeks).

   Since this material can be somewhat dry, we will regularly pull examples from the (introductory) material of the next chapter.
   As well, since the presentation in your text is somewhat brief, we have the supplementary book, div, grad, curl, and all that, which is very detailed and reviews well much of the material that you were supposed to have learned in Math. 311.

2. Ch. 2: Electrostatics: 1-13 February (2 weeks).

   Large portions, but definitely not all, of this chapter is review of material that I am sure you learned in introductory physics, as a freshman: applications of Gauss' Law, or equivalently, Coulomb's Law, to various sorts of problems where nothing depends on time. Nonetheless, reviewing it has value, and working the problems has even much more value, since it will provide the basis from which we begin to approach the new material in much of the rest of the text. We also use the time-independent version of Faraday's Law to create a potential function for the electric field.

3. The First Exam will be on Wednesday, 15 February, during the regular time of the problem session, and will cover Chapters 1 and 2.
4. Ch. 3:  Special (Mathematical) Techniques for Electrostatics: 15 February - 3 March (2 1/2 weeks).

   We learn new mathematical techniques to determine the requirements of Coulomb's Law in more complicated situations. Using the electrostatic potential, these amount to methods to solve Poisson's equation (or Laplace's equation) under various sorts of boundary conditions. We also study these equations in cylindrical and, especially, spherical coordinates, where Legendre polynomials become quite important, allowing us to define multipole moments of complicated charge distributions.

5. Spring Break occurs for the entire week of 12-18 March.
6. Ch. 4:  Electrical Fields in Matter: 6 March - 27 March (2 1/3 weeks).

   Inside materials we devise a separation of the electric fields into those dependent on "free charges" and those caused by the polarization of the "bound charges" that must stay close to where they originate, inside that material.

7. The Second Exam will be on Wednesday, 29 March, as usual during the time for the problem session, and will cover Chapters 3 and 4.
8. Ch. 5: Magnetostatics: 31 March - 12 April (2 weeks).

   Here we will concentrate on the similarities, and the important differences, between the magnetic problems and the electric problems. The additional physics comes from Ampere's Law, or, equivalently, the Biot-Savart Law, relating magnetic fields to currents. Many of the mathematical techniques are very similar to the electric ones. However, the zero divergence character of the magnetic field creates for it a potential, but one which is a vector field, therefore making problems more complicated than those for the electric field, where the potential was just a scalar function.

9. Ch. 6: Magnetic Fields in Matter: 14-21 April (1 1/3 weeks).

   Under the influence of magnetic fields, inside materials we have a separation into "free currents" and "bound currents", which allows us to devise now a separation of the magnetic fields into those dependent on the two sorts of currents. This also introduces diamagnetic, paramagnetic, and ferromagnetic materials.

10. The Third Exam will be on Wednesday, 26 April, during the problem session time, and will cover Chapters 5 and 6.
11. Ch. 7: Beginning Electrodynamics: 24 April - 3 May (1 1/2 weeks).

    Here we leave the domain of time-independent phenomena, and recall the very important changes that time dependence can play, in both Faraday's Law and the time-dependent addition that Maxwell made to Ampere's Law, justifying giving it a new name. Lastly, we look at these as a unit, constituting the set known as Maxwell's equations, all preparatory to a serious study of the time-dependent properties in the next semester.
    Much of this material is review from freshman physics, again. However, it was rather "tricky" then, so we need to see if we cannot understand it a little bit better this time through!

12. The last lecture class will be on 5 May, and will be an important Review Session for the semester.
13. The Final Exam will be on Monday, 8 May, at 10:00 am, for 2 hours. It will be comprehensive over the entire semester, with about 1/3 of the material concentrating on those subjects since the Third Exam.

Some Additional, General Notes On Your Text
The author of your text is very concerned that you, his readers, should acquire a well-developed intuition concerning how electromagnetic phenomena work. This is quite understandable, since both students and faculty tend to consider electromagnetism to be rather more mathematical than those subjects that students have encountered previously in physics.
There are several plausible reasons for this, which would include the following:

• all the important physical quantities are vector fields, depending on 4 different coordinates, x,y,z,t.
• the relevant equations involve partial derivatives, and partial differential equations,
• applications usually involve complicated boundary shapes, thereby introducing functions adapted to those shapes.

Some other, more specific comments:

1. He uses SI units, namely [m,kg,s,C], with only some reference in an appendix to the existence, and relationship, of Gaussian and Heaviside-Lorentz units. This approach is usual, although it can be difficult at times, either when one consults other books or goes further into a more advanced course, where Gaussian units are much more commonly used.
2. Most of physics involves
   observations of phenomena at some (field) point, located by some vector, say , relative to some choice of origin,
   caused by occurrences at some (source) point, denoted by some other vector, say , relative to the same origin.
   Therefore it is very common to be interested in the difference of these two locations. Use of a single symbol for this difference simplifies the appearance of the formulae, and also sometimes obscures the intent of the formula. Therefore most authors of texts use some special symbol for
   the vector from the source point to the field point,. Griffiths uses the symbol     for this difference, i.e., to mean - .
   I have difficulty duplicating his symbol on the blackboard in class and also in homework solutions; therefore, I will be using for the same purpose the Greek letter "xi", = - instead, although with an arrow over the top to remind us that it is indeed a vector.

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