Coulomb’s Law was actually a solution to Gauss’ Law, and in that sense Coulomb’s Law is redundant information. As a reminder, here are those laws:
F = R(hat) * ( (Q1*Q2) / (4πǫR^(2)) )
where F is the force exerted on a point charge Q2 by a charge Q1, and
integral(S) D · ds = Qencl
where Qencl is the total charge enclosed by the surface S. Prove that Coulomb’s Law actually is a solution as I claimed. Here are some tips: (1) Remember that electric ﬁeld intensity is – by deﬁnition – force divided by charge. (2) You’ll ﬁnd this easiest in spherical coordinates where charge is placed at the origin.