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Re: Flat conductors (was I need help).



Regarding John M.'s extended Maple calculations that went up to 11
dipole pairs:

...
I think you'll agree that the series appears to converge quite
well to a result that satisifes the required boundary conditions.

I also include revised 3-d views comparing the "11 pair" image
solution to the standard unbound 2-d dipole.

It appears that the results are indeed better than I had feared they
might/could/would be. I'm glad this image method works as well as it
does. Now I just need to think a little more about *why* this image
method works so well for a 2-d problem whose asymptotic potential for
individual charges is logaraithmicly divergent, whose asymptotic
dipole potential goes like 1/r, and whose quadrupole potential goes
like 1/r^2 in terms of the distance r . Hmmm. Maybe there is some
other symmetry in the problem that I hadn't considered that makes
things converge faster than I had considered. At the moment I can't
think of one off the top of my head that would seem to do the trick.

David Bowman
David_Bowman@georgetowncollege.edu