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Re: I need help.



Hi David:

I do not know where the 0.14 mm comes from. In the first
description of your geometrical method (2/19/02) charges
+Q and -Q were located at the focal points. In the yesterday's
message they are shifted by 0.14 mm toward the center of
symmetry. In practical terms this is not significant; I can not
locate equipotential points with an accurate less than 1 mm or
so. But I still want to know. Numerical illustrations are very
useful; they help to make sure messages are well understood.

Following your first description I proceeded as follows.
After measuring DOP=50 V at the point (14,10) I calculated
K=7/3 =2.333. This gives me the radius of the equipotential
circle = 5.250 cm. Where is the center of this circle? It is at
x=19+1.837=21.837 cm (and y=10). There were no 0.14 mm
shifting toward the center in this approach. What did I miss?
Ludwik Kowalski

David Bowman wrote:

Regarding Ludwik's latest report concerning his experiments
with equipotential curves on Pasco paper:

How could I resist and not to come to the lab and explore
things without being disturbed? Three important details:

1) For some reason the experimental line posted on my
website this morning was not positioned properly. I should
have compared the quickly plotted line with the numbers
from my notebook but I did not. Nothing substantially
different except the exact location of the line. Perhaps
my hand was still sleeping.

Ludwik, in case you are interested, I calculated the predicted
locations of a couple equipotential curves using the infinite sheet
formulae for the experimental situation described on your web page.
Assuming that you have two silver dots whose diameters are both
7.50 mm and whose separation between their centers is 100.00 mm
where the left dot has a potential of 0 V and the right dot has a potential
of 80 V, I calculated the theoretical location of the 'foci' and the
theoretically predicted equipotential circles for the 56 V, 50 V, and
30 V equipotentials (using the infinite sheet formulae).

If the left 0 V dot is centered at x = 90.00 mm & y = 100.00 mm and
the right 80 V dot is centered at x = 190.00 mm & y = 100.00 mm
then the 'foci' are each located 0.14 mm toward the center axis of
symmetry from the dot centers. This puts the coordinates of the left
'focus' at x = 90.14 mm & y = 100.00 mm, and puts the right 'focus'
at x = 189.86 mm & y = 100.00 mm. The *diameter* of the 56 V
equipotential circle is 57.85 mm, and its center is at coordinates
x = 197.64 mm & y = 100.00 mm. The *diameter* of the 50 V
equipotential circle is 108.90 mm, and its center is at coordinates
x = 213.83 mm & y = 100.00 mm. The *diameter* of the 30 V
equipotential circle is 108.90 mm, and its center is at coordinates
x = 66.17 mm & y = 100.00 mm.

If your 56 V, 50 V, and 30 V 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.