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What I think is wrong with your claim is your
assumption that between two points, the resistance
and the current paths have the same sensitivity.
The current path is the analog to field lines and
is related to the equipotentials. ....
.... Thus the current paths and the associated
equipotentials can be very different between the
finite and the infinite, but the resistances can
be almost the same.
Am I correct in understanding that in you
measurement of resistance as you cutdown the sheet
that the rings were 2.5 cm apart at the closest
point?
The near points dominate the resistance. Look
how much of the rings is within 5 cm of each
other. One would be tempted to consider this a
distorted parallel plate capacitor The 2.5 cm
separation is much smaller than the paper. If I
draw this and add a few current paths, and then
start "cutting down" the sheet, there are not that
many paths that get cut.
I am confused by your term "surface charges."
In the resistor-paper analog to electrostatics,
charges become current sources or sinks. Are you
saying that along a given ring, the voltage is
not functionally constant, i.e. the resistance of
the silver paint is noticeable relative that of
the paper?