The Coulomb law is the law governing the force between electrostatic charges.  Coulomb’s experiments with the torsion balance (above photo[1]) involved spherical surfaces and aimed to maximize electrostatic potential.  As electrostatic charge applied to the spheres, the force between the spheres would increase.  The charged spheres would then attract (if opposite charged) or repel (if like charged) and thus would move a specific distance.  Experiment showed that the distance squared was inversely proportional to the amount of the electrostatic charges:

$${k_C}\frac{{e \cdot e}}{{{L^2}}} = F$$

In the above equation, where k_C is Coulomb’s electrostatic constant, e represents the electrostatic charge, L is the distance between the charges, and F is the resultant force.

Coulomb noticed that the above law does not hold when the charges become very close to each other.  This is because the strong charge begins to take over.  The boundary between the electrostatic charge dominance and the electromagnetic charge dominance is gradual.  The balance between these two forces results in the weak interaction.

[1] Photo from http://www.wpcmath.com/arts/coulomb.gif