2) I did collect data on the geometry mentioned by Joseph.
The diameter of my ring was 220 mm while the diameter of
the central dot was 6 mm. I tabulated V(r) along four radii:
left, right, up and down. Numbers are consistent. The average
values of V(r), from four columns, are shown below.
I calculated |E|= dV/dx and plotted them versus 1/r. The resulting
straight line confirms what Joseph was saying, but only for r>2 cm.
I must collect more data at r<2 cm (smaller steps and averaging for
8 or more directions). The present value of E, between 1 and 2 cm,
is not on the straight line. This is an indication that something
unusual might be occurring at r<2cm.
3) And finally the paper size effect. I cut one inch of paper along
the top margin and along the bottom margin. Then I traced the
50 volts line. A small (hardly significant in view of the accuracy)
displacement of that line was observed toward larger discrepancy.
Cutting additional 1 cm strips, along the top and bottom added
additional small shift in the same direction. I was already very
close to the edge and expected (intuitively) a stronger effect. But
a strange thing happened when additional 2 cm strips were cut,
along the top and bottom. At that stage the margins were at y=3
and y=17 cm. The 50V equipotential lines became nearly the
same as it was before cutting anything.
I am confused by this observation. Perhaps what is observed
is a mixture of two effects: the paper size and something else,
for example surface charges near the edges. The progressive
large shift of the experimental line away from the theoretical (b)
line (when cuts are made) was not observed. The observed
displacements of the equipotential line (DOP=50 V) were
very small. My tentative overall conclusion is that the paper
size effect is not the main cause of the discrepancy. But this
is only a guess. The project is definitely to big for me. I am
glad tomorrow is not Monday.
Ludwik Kowalski