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: I need help.



John Mallinckrodt wrote:

As has been pointed out, the conductive paper imposes boundary
conditions that may be dealt with via an image charge technique.
I have asked Maple to do some calculations to help me visualize
the results. It was happy to oblige, but suggested that I share
its findings with the world. I like to keep my Maple happy, so
please see

<http://www.csupomona.edu/~ajm/special/condsheet.pdf>


John was replying to this:

.... I also believe that the final size is an important factor
but I can not prove or disprove it. The only thing I can
do is to show that there is big discrepancy. Only a
theoretical physicist can do this. The task is to compare
theoretical curves for the sheet of final size with those
calculated for the unlimited size. If the final size of the
sheet is the only factor then what is calculated for the
12" by 9" sheet should agree with what is observed
experimentally. The sheet thickness is very uniform
(always 0.013 mm) and rho=0.32 ohm*m. ...

I am also impressed. I hope everybody can see that what
I labeled as x and y is labeled as y and x by John. And that
only one half of the conducting sheet is shown; the other
part is symmetrically identical, as far as the shapes of the
equipotential lines are concerned.

Correct me if I am wrong, John. The boundary conditions
you are simulating (by placing several fictitious charged
cylinders outside the sheet) make the equipotential lines
nearly perpendicular to the margins of the sheet. In other
words you are forcing them to open by bringing five
mirror dipoles.

You are showing that a set of experimental equipotential
lines, on a sheet of certain size, can be made consistent
with the theory by manipulating fictitious charges outside
the sheet. This is impressive. But suppose you are not
familiar with experimental curves and you are asked to
make a prediction. How would you decide about sizes and
locations of fictitious charges? In other words, what is
your justification for making equipotential lines on the
carbon sheet perpendicular its margins? I suppose you
would say that the current near a margin must flow along
the margin. Right? But you are performing electrostatic
calculations and there is no current, only the E lines.
What prevents the E lines from crossing paper margins?
Ludwik Kowalski
P.S.
I suppose that fictitious charges correspond to real static
charges along the margins. Are we saying that the so-
called "paper size" effect is really the effect of static
surface charges, like those described by Chabay and
Sherwood? I see that Carl Mungan already made this
connection about one year ago (February 2, 2001).
If they play an essential role in wires then they should
also play a role in flat resistors.
Ludwik Kowalski