Fundamental Electromagnetism 7.5hp
This page can be found at
PhD course in Theoretical Physics at Lund University
Course book: J. D. Jackson, Classical Electrodynamics, third
Problems to attempt (useful for understanding the later chapters)
Hints and comments to some of the exercises
- Don't forget 1.6d on the next page
- The first printing had a different (and wrong) version,
use the latest one
- For part (a), it is much easier to prove for Cartesian
multipoles and then use the relation between the two types of multipoles.
- Part (c) can be solved via direct integration or by expanding in
ρ and z and using the symmetries of the problem plus Maxwell's
- Part c can be easily solved by remembering that integrating over
a sphere at a fixed radius r we have that
int dS n_i n_j f(r) = 4π/3 δ_ij r^2 f(r)
- It is enough to do it for one of the polarizations only, but note that
once you have done one, the other is not much more work.
- There are some overall phases missing in the answer given in part (a)
- Add the interpretation of the averaging used in part (c),
i.e. how you interpreted the expectation value mentioned.
There seem to exist two versions of (b) in the different printings.
The version you should solve is: repeat (a) but for an ideal conductor.
Do you get the same answer ?
- The notation of the answer in (a) is confusing but
correct. If you have problems, leave out the final integral over solid
- Beware you formula copiers, the current distribution is
not of the form in the chapter, but similar enough so the solution should
be doable. Final integral needed can be done numerically, it is feasible
analytically but a little messy.
Some comments of the students and other possibly useful hints
- I found the book by David J. Griffith,
Introduction to Electrodynamics,
useful as a help.
- The open course ware at MIT
(search for physics and/or electromagnetism).
- You can find many lectures on youtube as well. I found several
for electromagnetism lectures
- You can also try the more general
Open Courseware Consortium.
- Some nice graphical illustrations of some of the
principles can be found at
Solutions on the web
There are many places with solutions to problems in Jackson available.
The idea for you is to learn electrodynamics, not to figure out
how to find someonelse's solution. Try Google with
jackson+electrodynamics+solutions and you will find many problems solved.
But be careful, they are often wrong and/or have misunderstandings, so use them if you
cannot find the solution yourself but make sure you understand what's going on.
Last changed: January 2012