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Re: I need help.



Bernard Cleyet (speaking practically) wrote:

Skimming the below leads me to suggest that the effect of finite embedded
medium can be qualitatively detmnd by finding the equipotentials over a
larger area - especially near the edges. The %age where "fringing" is
evident (to the whole area for the sheet) is a measure of the error?

I like this suggestion because I know how to implement it.
I will measure the DOP at a point situated away from the
axis (where the discrepancy is very strongly pronounced)
and see what happens to this DOP when a margin of paper
are cut.

For example, at y=16 cm (which is 6 cm above the axis and
5 cm below the top edge of the sheet) the experimental line
is at y=20 cm while the theoretical line is at 17.6 cm.
Suppose I cut 1 or 2 cm of paper at the top. This will bring
the paper boundary closer to y=16 cm. If the DOP remains
nearly the same (which I now suspect will not happen) then
one would say that the paper size effect is not significant
for the chosen geometry. On the other hand, if the DOP
changes (probably in the direction of larger discrepancy)
then the effect of the paper size will be demonstrated.
Is this worth a trip to school? Probably not; I will do
this next week.

John Denker (speaking theoretically) wrote:

Bernard Cleyet conjectured that:
...
the effect of finite embedded
medium can be qualitatively detmnd by finding the equipotentials over
a larger area - especially near the edges. The %age where "fringing"
is evident (to the whole area for the sheet) is a measure of the error?

Well, using the periodic-boundary approach discussed
in my previous note, it is !!quantitatively!! determined.

The fringing _from_ this cell into the whole larger sheet
is exactly the same as the fringing _into_ this cell from
the neighbors. You just have to add up all the contributions.

This trick has been around since 1822.
http://www.google.com/search?q=fourier+analytique+chaleur