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If you search the archives of AJP you will find articles on
the role of surface charges. This is a very carefully written
insightful text and deserves your careful reading.
On Fri, 15 Feb 2002, Ludwik Kowalski wrote:
... here is a challenge to those who like to make predictions.
What kind of equipotential lines would you expect for the
silver strip painted on a carbon-impregnated paper if the
shape of the strip was an uncurling flat spiral. Suppose the
length is 100 cm, the DOP between the terminals is 1 V, the
uniformly distributed resistance of the strip is 1 ohm.cm and
the angle is 1800 degrees (5 round trips from the grounded
terminal at the center to the positive terminal at outer end).
Draw equipotential lines for U=0.5 V and U=0.25 V. Assume that
the resistance of the carbon paper, (for example ohms/cm^2) is
1000 times larger than that of the silver layer. Ludwik
Kowalski
Here's my entry.
<http://www.csupomona.edu/~ajm/special/spiral_ep.gif>
You'll see that I ran out of patience at two cycles, changed the
total DOP to "10", totally ignored the specific values of
resistivity, but included representative E-field vectors to
indicate the general character of the field.
Note in particular the dipole like field external to the spiral
and the related existence of a cusp in the equipotential lines
emerging from the interior as they choose which way to head
around the exterior.
John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm