Re: superposition

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Tue, 14 Jan 1997 kowalskil@alpha.montclair.edu wrote:

> Just thinking aloud about a superposition demo. Suppose you use carbon
> paper with two silver-painted spots and you measure E (grad of V) at a
> given location. Then you take another paper and the second spot is at
> another location. You measure E at the same spot as before and it is
> different. Finally you "superpose" by painting three spots on the third
> paper and measure E again. This should, in principle, be an easy way
> to show that E3=E1+E2 (vectors).
>                                      Ludwik Kowalski

Sounds like a practical demo, and is a neat use of the conductive
paper/paint apparatus. One of these days I must try it, for I'm always
looking for new ways to use this stuff.

But for those who do, here's some tidbits from my experience.

To measure the field gradient, tape two pointy meter probes solidly
together so their tips are a fixed distance apart, about 0.5 cm. Use the
voltage range of a digital meter, or mv more likely. The reading is then
proportional to the average field component between the points where the
double probe is pressed to the paper. Fiddle with different orientation of
the probes to get a maximum reading, and you've found the direction of the
field, and its size in volts/cm.

Resistivity of the paper itself can be a problem. Turn it to your
advantage. Measure the resistance of strips cut from the paper of
different widths. Try different shapes (a strip with varying width, for
example). Resistance of two strips in series. In parallel. Could
substitute for the old resistivity experiment with wires of different
diameters on a board. A clip-board can hold one end of the strip.

Experiments are often done with this paper to simulate electric fields and
equipotentials. Students are seldom reminded that this resistive paper
medium gives rise to a field with *cylindrical* symmetry, hence one cannot
expect E = kq/r^2, but should get E = kq/r. Makes a difference! Worth
investigating on its own merits.

How about studying a conductive pattern consisting of just one small spot
of conductive paint, and a large circle of conducting paint centered on
it, as large as the paper will allow. The field should be radial, and easy
to deal with. Now investigate the field strength as a function of radial
distance from the center spot. It is approximately 1/r. The potential goes
as ln r. But not exactly. There's charge in transit from the center
outward. At any distance, r, the charge enclosed by a Gaussian surface is
that of the center electrode plus that in the paper with the circle of
radius r. How does that affect the field and potential variation with r. 

See how this simple apparatus can even lend itself to an *advanced*
experiment?

	-- Donald

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Prof. of Physics                    Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745          CIS: 73147,2166 
Home page: http://www.lhup.edu/~dsimanek            FAX: 717-893-2047
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