Justification for the acceptance of Coulomb's law

[Vinay080]

I read the Coulomb's first memoir on Electricity and Magnetism (Louis L. Bucciarelli english translated version), and found it to contain only three trials (as complained by many) to reach the conclusion of a 1/r² equation for the force. And many seems to have also complained for not having able to get the same results. I read the recent papers of A.A Martinez and others who have tried to reproduce the experiment (the technical details went beyond so I couldn't complete).

What I want to know now is, what has made Coulomb's law unquestionable? Has the experimental justification for the law been given? What are the reasons for accepting it?

Or is the same equation been arrived theoretically (I have a feel for this)?

I have asked the same qeustion in other physics website to have faster clearance of problem.

 

[Vinay080]

I have found the relation w.r.t Gauss law. Now the question is whether Gauss law was arrived with the help of Coulomb's law or with the help of experiment or with the help of other means?

 

[blue_leaf77]

Assuming the law to be violated by a small exponential parameter $r^{-2+\epsilon}$, a work done in 1970 documented in https://www.princeton.edu/~romalis/PHYS312/Coulomb Ref/BartlettCoulomb.pdf found that $|\epsilon|$ to be on the order of -13. That paper also has a list of $|\epsilon|$'s measured prior to their measurement (jump to the last paragraph before acknowledgment section).

Now the question is whether Gauss law was arrived with the help of Coulomb's law or with the help of experiment or with the help of other means?

Gauss law is a consequence of the central nature of the inverse square law.

 

[alw34]

I'm not sure it's unquestionable, but it works well enough to be useful.

As r approaches zero, things go awry.

 

[SammyS]

Assuming the law to be violated by a small exponential parameter $r^{-2+\epsilon}$, a work done in 1970 documented in https://www.princeton.edu/~romalis/PHYS312/Coulomb Ref/BartlettCoulomb.pdf found that $|\epsilon|$ to be on the order of -18. .

Unless I misread that paper, $\ |\epsilon|\$ is on the order of 10⁻¹³ .

 

[blue_leaf77]

Unless I misread that paper, $\ |\epsilon|\$ is on the order of 10⁻¹³ .

Sorry, I think it was because old print effect. Upon 175% zooming in, I agree with you that it should have been 10^-13.