Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: I need help.



As has been pointed out, the conductive paper imposes boundary
conditions that may be dealt with via an image charge technique.
I have asked Maple to do some calculations to help me visualize
the results. It was happy to oblige, but suggested that I share
its findings with the world. I like to keep my Maple happy, so
please see

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

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

On Sun, 24 Feb 2002, Ludwik Kowalski wrote:

David's message forced me to ask why my theoretical (b) line
was so different from his. I went to my little True Basic
program and found a bug. Now my numerical method and
David's geometrical method produce the same circle. This
forced me to replace the figure posted at my website:

http://blake.montclair.edu/~kowalskil/elec/eqp1.html

Yesterday David wrote:

If your equipotential curves do not come close to these
predicted circles it can be taken as evidence that the finite
size of the paper is significantly distorting the equipotential
curves by artificially restricting the region of conduction
to a smaller region than is the case for an infinite sheet.
Another possible confounding effect is the possibility that
the paper's conductivity is somewhat inhomogeneous as well.

The fact that vertical and horizontal symmetry is displayed by
curves on several different sheets seems to indicate that the
inhomoginities are not a factor. I also believe that the final
size is an important factor but I can not prove or disprove it.
The only thing I can do is to show that there is big discrepancy.
Only a theoretical physicist can do this. The task is compare
theoretical curves for the sheet of final size with those calculated
for the unlimited size. If the final size of the sheet is the only
factor then what is calculated for the 12" by 9" sheet should
agree with what is observed experimentally. The sheet thickness
is very uniform (always 0.013 mm) and rho=0.32 ohm*m.

But I will ask students to explore smaller distances between
silver circles (for example, 8 or 6 cm instead of 10 cm). If the
discrepancy goes away, or is reduced significantly, then the
final size effect would be demonstrated. What else can one do?
Bernard's suggestion was tried yesterday (see the message I
posted last night) but it did not help to clarify the issue.