Concluding Remarks About Multipoles

There are still many, many things we could study concerning multipoles and radiation. For example, we have not yet done a magnetic loop antenna, but doing one should now be straightforward (to obtain a magnetic dipole radiation field to leading order). Hmmm, sounds like a homework or exam problem to me...

Still, I hope that this has left you with enough fundamentals that you:

1. Understand bessel functions;
2. Understand spherical harmonics;
3. Understand at least something about vector spherical harmonics;
4. Know what a ``multipolar expansion'' is;
5. Know how to expand a variety of important Green's functions for vector and scalar Helmholtz equations (including the Poisson equation).
6. Know how to formulate an integral equation solution to these differential equations based on the Green's function, and at least formally solve it by partitioning the integral into domains of convergence.
7. Know how to describe the electromagnetic field at a variety of levels. These levels had better include the elementary description of the E1, E2, and M1 ``static'' levels as well as enough knowledge to be able to do it correctly for extended sources or sources where higher order moments are important, at least if your life or job or next paper depend on it.
8. Can pass prelims.

If you feel deficient in any of these areas, I recommend that you take the time to review and learn the material again, carefully. This has been the most important part of the course and is the one thing you should not fail to take out of here with you.

I hope you have enjoyed it.