Re: I need help.

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

Roger Haar wrote:

> 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.

That is a possibility worth investigating. Let me think
about this.

>  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?

My silver-pained areas were circles of 7.5 mm diameter.
The rings would produce the same field, I suppose, but
I did not use rings. The distance between the centers of
my circles was 10 cm, not 2.5 cm. But, as I indicated,
exploring smaller distances for the sheet of the same
size may produce additional evidence for the claimed
discrepancy. Suppose I reduce the distance to 8 or 6 cm
and find out that equipotential lines have the same shapes
as for the 10 cm. Would you then be convinced that the
sheet is sufficiently large to produce the same lines as
the infinitely large sheet? I will ask students to explore
the reduced and the expanded (going from 10 to 12 cm)
geometries. Is it worth doing?

> 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 not sure this applies to my 7.5 mm circles
separated by 100 mm.

> 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?

In this context the term "surface charges" was used
instead of "hidden causes", "devil" or "who knows what."
Something funny takes place and I need something to be
responsible for it.

If it is true that surface charges are necessary in wires to
bend electric lines locally then they are also necessary to
bend the E lines in a conducting sheet. Is this a reasonable
expectation? If not then why not? It is a separate answer
worth discussing under the Chabay/Sherwood thread.
Ludwik Kowalski