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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 $1/r^2$ 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)?

Qmechanic
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Sensebe
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    @Qmechanic: Thanks for Gauss-law! Now I am wondering how gauss law was reached, whether independent of Coulomb's law or with the help of it or with the help of experiment... – Sensebe Dec 20 '15 at 10:22
  • I have asked the same question in other physics website to get greater help. I will be commenting on the development from all the sources. – Sensebe Dec 20 '15 at 10:36
  • I found a helpful question, but I didn't find answer helpful: http://physics.stackexchange.com/q/161984/ – Sensebe Dec 20 '15 at 11:15
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  • Interesting question. 2) IMHO you should change the title to "What were the reasons for accepting Coulomb's law?": in the present there are plenty of experimental and theoretical reasons to accept it. The real questions is why did they accept it at the time of Coulomb, as back then there were very few reasons. 3) If you dont get useful answers here you could try luck at http://hsm.stackexchange.com/
    • – AccidentalFourierTransform Dec 20 '15 at 11:43
  • I'm hopeful that there will be answers from a historical point of view. I'm not satisfied with the law in infinite distance. This is because I'm sure that the electric field, the magnetic field and EM radiation is quantized and that means that there are quanta with finite energy content and a structure from such quanta has to be finite. More see here about complex one-dimensional structures of space. – HolgerFiedler Dec 20 '15 at 11:49
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    Possible duplicate of Precision of Coulomb's law – ProfRob Dec 20 '15 at 12:14