Reason the coulomb force is a function of r such that he integrant can put into a form of a total (exact) differential d(1/r) Implications: by Stokes'Theorem ∮E·dl=/(V×E).da=0, since the path has been arbitrary thus we find that V×E=0 i. e, an electrostatic field has no curl Moreover. a cur -less vector field. such as e. can be written as a gradient of some scalar function, say, E