- The wording of Problem 1.12 suggests use of a calculator. If your calculator will do this, fine. If not, maybe check some 18.03IS-ESG notes, Finding Roots Using MAPLE Release 9, Xdvi or PDF.
- Problem (C) mentions functions being
"sufficiently differentiable," but the phrase is not explained in
detail. Besides assuming you can differentitate to any order, you
need also to assume the following:
There aren't as many problems as in the first set, but the quality accounts for the difference.
- Problem 1.35 from Purcell is just great. The
physics behind the problem is one of the most important things we'll
see, and the math involved, admittedly difficult, is of the sort that
will help you immensely in other physics subjects.
Not kidding on that one. Keep working on it until you get the result, write it up neatly for your own benefit, and save your work as long as you do anything in your life related to physics.
For some hints at the math, seePurcell 1.35 Hints . - The extra problem, dealing with the field due
to a dipole, requires the proper form for the potential. This will be
done in class on
Friday September 24 , which is part of my sneaky way to make sure everyone, including me, shows up.
Mention is made of making sketches of field lines. I'm not interested in really good sketches - that will come later. If, however, you wish to use MAPLE to do the sketches, you'll want the fieldplot feature. Details upon request.- Full disclosure: My experience is that it takes much more effort than it's worth to make really good field plots, especially when the magnitude of the field diverges. There are some tricks, but that's not what we're interested in at this point.
- Those dipole fields won't go away. They had better not; every molecule of water has one.
By doing some vector calculus at the beginning of the term, we've already seen some of this. Depending on how much you really like vector derivative operators, the following OPTIONAL Supplemental Notes may be of interest.
- Coordinate-Free Representations of Vector Derivative Operators
- Leibniz' Formula with gaudy colors.
Not much new, due to the adjusted quiz schedule. Mainly math, which will be good practice for the quiz.
The cited notes are "Dipoles" in 2 Dimensions, XDVI or PDF. Any dates cited in these notes are clearly obsolete.
The cited notes are Image Charges for Conducting Spheres. The template we'll be using for Problem 4.27 from the text is at Template for DC Circuits (download with "Shift-Left-Click" or "Right-Click".)
The cited notes are Non-Simultaneity in Moving Frames, presented mainly because I don't want to keep drawing those figures in chalk.
- Chapter 6: 3, 4, 8, 12, 16 (have you seen something like this before?), 19 (this has stumped some pretty smart folks around here),22, 25, 33.
- Chapter 7: 4, 6, 9, 11, 14 (this involves solution of a separable differential equation), 17, 27 (more conceptual than mathematical), 29 (a really neat one, well worth your effort), 30 (you were warned that this was coming), 31.
- Chapter 8: 4, 5, 7, 16.
- Chapter 9: 5, 8, 9, 10, 13.