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Re: Flat conductors (was I need help).



I told Maple about David's skepticism regarding my 5 image dipole
solution to the conductive paper dipole experiment. See

<http://mailgate.nau.edu/cgi-bin/wa?A2=ind0202&L=phys-l&F=&S=&P=103852>

and it responded with a series of results of the following form

... - - - ...

... + + + ...

-----
| |
... + | + | + ...
-----
... - - - ...

The box shows the region in which the potential is being
determined and the set of image dipoles extends off to the left
and right symmetrically. The arrangement shown above shows "3
pairs" of dipoles, the arrangement used for my previous results.
Maple continued the series up to 11 pairs. This arrangement
guarantees the required boundary condition along the top edge of
the region but only approaches the required condition along the
side as the number of pairs of image dipoles increases.

In each case the simulation region is 14 units wide (x) by 20
units high (y) and the positive line source is at (0,5). I
normalized each result by multiplying it by a factor and then
subtracting a constant with the factor and the constant chosen in
order to force V(0,5.5)=10 and V(0,0)=0. Then I included
potential contours at 1/2 unit steps up to 10. The results are
shown at

<http://www.csupomona.edu/~ajm/special/condsheet2.pdf>

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.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm