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It seems to me that the problem you are having with this, Ludwik, is
that your measurements are compomised (when trying to confirm the
exact theoretical solution) by the fact that your carbon paper is
a finite sized rectangle, rather than an infinite plane. Please
go back and look at the numerically calculated equipotential curves
calculated at Noah Gintis's URL that Brian W. mentioned:
http://www.nova.edu/~gintis/vlabs/overview/ef.html .
These calculations are *precisely* for the case of a finite
sized rectangular conducting region. Notice the shape of the
equipotential curves around the outside of the circle electrodes.
They are *not* circles. Instead they are flattened along the
directions parallel to the paper sides, and have the symmetry of
the paper itself. My exact solution for the infinite sheet problem
has no such finite size boundary effects, and its equipotential
curves outside a conducting circle are all exactly circular in
shape whether or not there are one or two charged conducting
circles present.
The most important contribution, at this time is to check
my conclusion; no experiment can be taken seriously
unless it is confirmed by others. Spend 15 minutes after
the lab is set for students and report your findings. (But
make sure R of the voltmeter is at least ten megaohms.)
Ludwik Kowalski
Or you can just look at the calculation (Gintis's) that is
appropriate for the actual geometry of the actual experimental
situation.