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Re: I need help.



Hi,
The "dipole" pattern produced on reistor paper is
like a slice of 3d space from 2 infinite rods.
The current only has 2d to spread out on with the
paper. The same is true of flux lines for the
infinite rods.

Trying to make exact comparisons between the most
shapes on the paper and the real world is a
problem. The edge of the paper effect will mess
up most patterns. In the case of the "dipole",
the corrects can be found using the method of
images. For the first order correction, instead
of two rod like

|------------------|
| |
| + - |
| |
|------------------|


One can find the field in the center sheet for


|------------------|
| |
| + - |
| |

|------------------|------------------|------------------|
| | | |
| - + | + - |
- + |
| | | |

|------------------|------------------|------------------|
| |
| + - |
| |
|------------------|

This arrangement pretty well confides field lines
to the sheet of origin. Higher corrections are
more sheets.


One can get consistent patterns if one uses a
parallel plate capacitor that goes from edge to
edge, but this is boring. We use two concentric
circles on the paper that is the 2d analog to
coaxial cables. The students easily find that the
field between the circles is logarithmic.


Thanks
Roger Haar

*********************************************
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