Re: Flat conductors (was I need help).

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

John Mallinckrodt wrote:

> On Thu, 7 Mar 2002, kowalskil wrote:
>
> > Why should the gradient be parallel to the paper boundary
> > everywhere, as it seems to be?
>
> Hint: Think about what the electric current would look like if
> this were not the case.

1) Please confirm that I understand you correctly. You were
solving an electrostatic problem to make a prediction about
the distribution of equipotential lines in a flat conductor.
The boundary conditions of the electrostatic problem were
set up to make make its predictions to be valid when the
current is flowing. If you were interested in the distribution
of equipotential lines on a non-conducting sheet the boundary
conditions would be chosen differently.

2) I do not know when I will have time to verify what I clearly
observed this morning. So let me describe it now. Perhaps
others will go ahead and explore the phenomena. But let me
quote Justin and Paul first.

Justinn Parke asked, "Does an electric field always exist
between the terminals of a battery?" Paul Johnson answered:

> If a wire is connected between the terminals, the situation
> is obviously no longer static. A potential gradient exists
> along the wire and field lines run along the gradient pushing
> free electrons uphill. They constitute the current that flows.
>
> Field lines also exist outside the wire. They bulge out from
> the wire's surface, their spacing indicating decreasing field
> strength with increasing radial distance from the wire. They
> go from points of higher potential on the wire (nearer the
> positive battery terminal) to points of lower potential (nearer
> the negative terminal). The field lines display cylindrical
> symmetry around the axial wire.

Here what I did. I took 5 strips of Pasco papers (each 3 cm
wide and 8 cm long) and used the silver paint as a glue. The
strips were glued along the 3 cm edges (to connect five flat
resistors in parallel) and the set was glued to the regular
Pasco sheet. The distribution of DOP along the setup was
essentially uniform. I was interested in the shapes of the
equipotential lines inside and outside the strip.

Inside the strip all equipotential lines were strictly parallel
to 3 cm edges. And what did I observe outside the setup
(on Pasco paper )outside the five resistor? The observed
equipotential lines are with asterisks below. The sudden
bending of the equipotential lines was observed outside
the strip, except along the central bisector.

             *           *           *
               *         *         *
                 *       *       *
      -------------*-----*-----*-------------
                   *     *     *
                   *     *     *
    3 cm           *     *     *           3 cm
                   *     *     *
                   *     *     *
      -------------*-----*-----*-------------
                 *       *       *
               *         *         *
             *           *           *

Please verify this observation. Please join me in experimental
explorations and share your results. May I suggest one particular
line of study: how does the "bending angle" depend on the number
of "flat parallel resistors?" (Silver ink costs $17, a set of 100
sheets of Pasco paper cost s $30. You probably already have a
good voltmeter. A very inexpensive student research project?
Why not? Physics is also an experimental science.)

Will the Currier font preserve the above diagram? I hope
so. The horizontal line are strip boundaries. What is
above and below them is a single layer of Pasco sheet.
The angle shown above is exaggerated; it was like 20 or
30 degrees, not 45 degrees. The bending angle increases
as one moves away from the central bisector.
Ludwik Kowalski