Comment by nh23423fefe
2 days ago
I feel like that should be gettable from rotational symmetry and somehow mentioning L2 norm to get the square. Either that or conservation of E-field flux.
2 days ago
I feel like that should be gettable from rotational symmetry and somehow mentioning L2 norm to get the square. Either that or conservation of E-field flux.
Rotational symmetry or L^2 norm only matter in vector formulations. I assumed a scalar formulation.
Conservation of E-field flux certainly implies additive-homomorphism (addition of charges equals addition of forces). But that seems a bit ahistorical because Maxwell would develop field theory 70 years after Coloumb. Either way, the axiom you choose requires empirical justification, and I think a home hobbyist could more easily demonstrate by experiment that adding charges will add the forces.
Or, if you meant F(r,1,1) = K/r^2, then yeah, conservation of E-field flux could give you an inverse square law. But again, that requires an experiment to justify the axiom.