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Re: I need help.



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.

2) I did see how cutting more and more slices affects the
location of the 50 V equipotential line. The first impression
is that the paper size effect is negligible. But wait for the
confirmation.

We'll see.

...

David Bowman
David_Bowman@georgetowncollege.edu