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Re: Bar magnets



John Denker suggests motion restraints for a coulomb balance used to measure
attractive forces. I was assuming motion restraints have been ruled out. I
thought the question was whether we can attain a stable equilibrium. I am
well aware of "flip-flop" or astable null detection and have used it many
times.

According to my definition of the problem, restraints to limit motion don't
count. If these do count, we can do the same thing with the original
question concerning bar magnets. Put spacers between the two magnets to
keep them from snapping together. These spacers are as thick as the
separation for which we want to know the attractive force. If we don't want
spacers between the magnets to change the permeability of the gap there are
ways around that. In any event, once the magnets are held together by
magnetic attraction at fixed separation, pull the opposite end of the spring
and notice the stretch of the spring just before the suspended magnet snaps
away from the other magnet. (Which it will do, i.e. snap away.)

Tim Folkerts asks about the Cavendish balance. This is the other situation
I mentioned, the torsion wire is too stiff (compared to the attraction
between the balls) to allow the balls to snap together. Here a null can be
achieved but we can't make a good static measurement because the deflection
is so small. This experiment is usually done dynamically... the suspended
balls oscillate as a torsion pendulum... static stable equilibrium is not
measured.

I stand by my original statements. If the detection system is sensitive
enough that it could move far enough to provide a static measurement with
meaningful precision, stable equilibrium will not be achieved and the
objects will snap together. The system can be made less sensitive to
prevent snapping together, but then it won't give the needed sensitivity in
a simple static-null measurement.

I assume we are discussing a position-dependent restoring force in the
measuring instrument, and the position dependence of this restoring force
appears in the force equation with a smaller exponent than the exponent of
the position in the attractive force we are trying to measure.


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