Reason the coulomb force is a function of r such that the integrant can put into a form of a total(exact) differential d(1/ r) Implications: by StokesTheorem ∮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=-VV