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: Flat conductors (was I need help).



John Mallinckrodt wrote:

On Tue, 26 Feb 2002, Ludwik Kowalski wrote:

To see the equipotential lines A, B, C and D plotted, and
compared with simple theoretical lines, click below.

http://blake.montclair.edu/~kowalskil/elec/eqp2.html

Your experimental data generally reflect the type of distortion
that would necessarily be caused by the existence of the
boundaries, but they also appear to be in pretty significant
disagreement with the theoretical requirement that the
equipotentials be perpendicular to the edges of the paper. Did
you measure carefully right out to the edge to see if the lines
become perpendicular?

Yes, the main purpose of repeating the measurements was to
focus on what happens at the margins. The extensions of lines
A, B and C (below the x axis on Pasco paper and on my plot)
show what happens when one goes to the very edge of the paper.
But it would be useful to have an independent confirmation.

The image charge calculations I did assumed a potential difference
of 10 units between the midplane and what is essentially a circle
of diameter 1 unit centered 5 units above the midplane. I chose
dimensions of 20 x 14 for the half sheet to match your drawings.
Translating my results to a 300 V potential difference between the
poles (and assuming that you used circles of 1 cm diameter for
your poles), my results would suggest that the potential at the
intersection of the dipole axis and the paper edge should be about
222 V, that the potential of either corner should be about 213 V,
and that the potential half way between a corner and the 150 V
midplane should be about 200 V.

On the basis of these results, I'm going to guess that your
circles are actually smaller than 1 cm in diameter, but that
wouldn't be quite enough to explain what appears to be some pretty
significant equipotential shape discrepancies especially in the
case of your 187 V line.

You are correct; the new circles are smaller. I will tell you tomorrow
how large they are on the Pasco sheet which was used this time. It
will probably be close to 0.5 cm. I am surprised to learn that exact
diameters of circles are still important when the distance between
their centers is as large 10 cm. Let me know what data you might
need to make further progress. For example, I can triple the
diameters and see what it does to the 187 V line.
Ludwik Kowalski.