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Re: Coulomb's law



in other words you want the functional relationship of epsilon
(r^-(2+epsilon)) to the internal field in order to propagate the
uncertainty.

one could do it roughly (w/o integration) using the common symmetry
argument used to show there is no field inside due to an external
charge.

BTW the sphere doesn't have to be spherical, just makes the arguments
and calcs. easier.

bc

Check out Plimpton and Laughton's (1936) work -- they obviously did it.
How did Max do it? I did find:

http://www.arts.richmond.edu/~rubin/pedagogy/132/132notes/132notes_71.html

but no Plimpton -- need a better engine. I notice the right wing
Republicans don't believe in the inverse square law. (published in "The
Federalist") http://members.tripod.com/~american_almanac/inverse.htm



Ludwik Kowalski wrote:

Most textbooks report that the factor n=2 (in the 1/r^n, appearing
in Coulomb's Law) can be determined by confirming zero field
inside a cavity surrounded by a conductor. Zero field is predicted
by Gauss's Law (derived from Coulomb's Law, where n=2.)

Suppose a small metallic sphere, say R1=10 cm, is placed inside
a large metallic sphere, say R2=20 cm. The two spheres are well
insulated. A potential V = 1000 V is applied to the outer sphere
and an attempt to measure the difference of potentials between
the two spheres is made. The result is that dV=0 +/- 0.001 V.
The ratio dV/V is thus 10^-6. How could such outcome be
translated into the "experimental error" for n=2.

I suppose that the most direct answer (n=2 +/- 0.000001)
would be wrong. Maxwell's estimate of the uncertainty
about n=2 is often reported as 0.0004. His spheres were
concentric. Is there a simple way of translating the dV/V
into the uncertainty about n=2 for two concentric spheres?
What would the correct uncertainty be (instead of the
0.000001) for my hypothetical example?
Ludwik Kowalski