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Re: Coulomb's force lab



Thanks for the tips, Michael. I forgot to mention that exploring
the limits of accuracy of Pasco balance is a research project of
our students, Carola Springer. We would very much like to
hear from other users of the apparatus, even if their experience
is identical to that of Michael. Write to us in private, if you
prefer.

We did the calibration yesterday afternoon. The curve is nearly
identical with that shown on page 15 of Pasco's Instruction
Manual. On the other hand, I am trouble by the small angle
(average 37 degrees) when both balls are fully charged and the
separation is 6 cm. According to what is shown on page 15
(and in Pasco 2002 catalog) the angle should be about four
times larger. How large angles do you observe, Michael,
under similar conditions? Unfortunately, we have only one
setup. Perhaps our power supply is not delivering what is
expected. We will share more next week.
Ludwik Kowalski

Michael Edmiston wrote:

I tried to send the following post yesterday, but it may not have worked. I
apologize if you have already received it.

* * * How we check Coulomb's law and the Coulomb Constant with the Pasco
Coulomb Balance * * *

To measure the permittivity (or the Coulomb constant) the torsion balance
has to be calibrated so we can convert torsion degrees to newtons. This
requires the balance be put on its side and calibration weights added to the
ball. I decided not to have the students do this because I was afraid it
would take too long and they might break the torsion wire. I demonstrated
it, then I did it and posted the result. I put calibration masses of 5, 10,
20, 50, 70 mg on the ball. I plotted force in newtons versus rotation in
degrees. The slope of the graph is the conversion factor
newtons-per-degree. This graphical method means accurately zeroing the
balance is not necessary.

I have the students do the permittivity by a similar process, and I have
them do it two ways. In one experiment they use a fixed separation, a fixed
charge on one ball, and vary the charge on the other ball. In the other
method they put the same charge on both balls and vary the separation.

For the first method they plot force versus the charge on the varying-charge
ball. This should give a straight line verifying force is directly
proportional to charge. They get the permittivity from the slope. The
balance does not need good zeroing because any zero offset shows up as
non-zero intercept; i.e. slope is not affected. They typically get the
accepted value to within 5%, many get it within 2%. The fixed separation is
about 10 cm. Much further and the forces are smaller. Much closer and
separation errors become more significant.

Some students don't appreciate the graphical method and want to calculate a
permittivity for each data point then average them. This means the balance
zero must be good. I beleive that ends up being a significant error for
some. But most important, I want students to realize how wonderful it is if
a desired parameter can be obtained from a slope and instrumental problems
appear in the intercept rather than the slope.

When students give both balls the same charge and record the force for
varying separations, I have them plot these data as force versus the
reciprocal-squared-separation. A straight line here demonstrates the
inverse-square behavior for separation. Again, the permittivity can be
obtained from the slope. In this case the students typically get worse
results, more like 10%.

I think the problem has to do with the separation not being well known, and
even being off by different amounts at different separations. Since the
charge can migrate on the balls, the center-to-center separation of charge
is larger than the center-to-center separation of the balls. The Pasco
directions give a correction formula for this. The students apply this
correction, otherwise the results are really terrible. But the correcton
formula must not totally solve the problem.

My students think I am the graph czar, or at least a graph fanatic. They
presume I have graphs of my children's height, my natural gas usage, etc.
I'm not that bad, but getting conversion factors and other parameters from
the slope is really a good way to go if you're not already doing it.

P.S. I am bothered that the Pasco correction formula for separation is
applied to the force. Each year I think I will work through the correction
and derive it for application to the separation, which would make a lot more
sense to the students. But I never have followed through. Has anyone
already done this derivation?

P.P.S I think the Pasco type of power supply gets to the "proper voltage"
within 2-3 seconds. We turn it on and use it right away. The torsion
balance is heavily magnetically damped and that does mean the measurement
cannot be made too quickly. But my feeling still is that we can read it
without waiting more than 10 seconds.

Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817