Re: I need help.

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding Ludwik's carbon paper problem:

> This experiment is a convincing evidence that the electric field
> in a flat conductor is the same as that produced by a uniformly
> charged rod of infinite length. It is very different from the E
> due to a point charge.

Joe Bellina's evidence clearly shows that, as expected, the paper
acts as a 2-d world (or a 3-d world with infinitely long
conductors in the dimension perpendicular to the paper).  But
since his measurements were specifically for the region between
two concentric circles, the finite size effect of the finite
paper size had no effects on those measurements.  This is *not*
the case for measurements taken outside the shielding effects of a
'boundary ring' electrode.

> Taking this for granted, David Bowman used the superposition
> principle to predict the shapes of equipotential lines. He wrote:
>
> > Now since the "difference of the logarithms is the logarithm
> > of the quotient" we can re-write the potential as
> > V = V_0 - C*ln(r_A / r_B).
>
> Unfortunately, experimental equipotential lines contradict
> this expectation. Why is it so? Please help to solve the puzzle.

It seems to me that the problem you are having with this, Ludwik, is
that your measurements are compomised (when trying to confirm the
exact theoretical solution) by the fact that your carbon paper is
a finite sized rectangle, rather than an infinite plane.  Please
go back and look at the numerically calculated equipotential curves
calculated at Noah Gintis's URL that Brian W. mentioned:

http://www.nova.edu/~gintis/vlabs/overview/ef.html  .

These calculations are *precisely* for the case of a finite
sized rectangular conducting region.  Notice the shape of the
equipotential curves around the outside of the circle electrodes.
They are *not* circles.  Instead they are flattened along the
directions parallel to the paper sides, and have the symmetry of
the paper itself.  My exact solution for the infinite sheet problem
has no such finite size boundary effects, and its equipotential
curves outside a conducting circle are all exactly circular in
shape whether or not there are one or two charged conducting
circles present.

> The most important contribution, at this time is to check
> my conclusion; no experiment can be taken seriously
> unless it is confirmed by others. Spend 15 minutes after
> the lab is set for students and report your findings. (But
> make sure R of the voltmeter is at least ten megaohms.)
> Ludwik Kowalski

Or you can just look at the calculation (Gintis's) that is
appropriate for the actual geometry of the actual experimental
situation.

David Bowman
David_Bowman@georgetowncollege.edu