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Coulomb's law



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