Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: I need help.



Since the flow lines all lie in the plane of the paper, it seems to me
that the situation is a 2 dimensional one.
Let me describe an experiment I did some time ago which supports this
claim.
Construct a ring of conducting paint, and put a dot of conducting paint
in the center. Measure the potential as a function of distance from the
center, plot the curve, differentiate it by drawing some tangent lines,
and then plot the slopes as a function of distance on log-log paper. Of
course now you would do it with a computer. The slope of the resulting
line is -1, so the electric field falls off as 1/r, which is the
characteristic of an infinite rod. In this sense the paper can be
seen as a perpendicular cut in the space around a charged rod.

cheers,

joe

On Tue, 19
Feb 2002, Ludwik Kowalski wrote:

Why is it so?

A standard student experiments with Pasco sheets is to
trace equipotential lines. But how well do these lines
agree with the theory? And which theory should they
agree with? I see two options:

a) Filed is like that of a dipole (two spheres in 3-D)
b) Field is like that of two long cylinders (dots are
the cross sections of these cylinders).

The second theory can be objected on the ground that
there are no long cylinders in this setup.

The first can be objected because the medium in which
the current is flowing is 2-dimentional.

To proceed I made predictions based on each theory and
compared them with the shape of the experimental trace.
Fortunately, the two predictions are very very different.
The bottom line is that neither (a) not (b) agree with my
experimental results. Let me illustrate this by providing
the (x,y) coordinates of the three lines. You have to trace
them on a graph paper to see what I mean.

But first some experimental details. The two silver circles
were at (9,10) and (19,10); they were separated by 10 cm.
The DOP of 80 V was applied and the current was about
2 mA. The voltmeter of 10 megaohm was used to measure
potentials (with respect to the left dot) at various locations.
As I indicated in the previous posting, the infinite sheet
approximation is applicable for this geometry.

To illustrate my point (and to minimize your efforts) I will
focus on only one line, the line passing through the point
(16,10), on the axis. The axis is at y=10. The point selected
is 7 cm from the left dot and 3 cm from the right dot.

The experimental equipotential line (DOP=50 V) is
symmetrical with respect to the axis (as it should be) and it
passes through the following points: (22.17), (20,16),
(18,14), (16.2,12) and (16,10).

The theoretical line (a) passing through (16,10) also passes
through: (21.5,13), (19,13.6) and (17.6,13).

The theoretical line (b) passing through (16,10) also passes
through: (21.5,13), (19,13.6) and (17.6,13).

Neither (a) nor (b) are correct. What theory should agree with
the experimental data? Comments will be appreciated.
P.S.
Suppose I am verifying Coulomb's Law using two charged
pucks on the air table. This is also a 2-dimentional medium.
I think that the 1/r^2 relation would be observed. On that basis
I would expect the potential to be proportional to 1/r, as in
3-dimentional space. Translating this into what happens on
the carbon paper I would expect the (a) prediction to be valid.
But it is not valid. Where am I wrong?
Ludwik Kowalski


Joseph J. Bellina, Jr. 219-284-4662
Associate Professor of Physics
Saint Mary's College
Notre Dame, IN 46556