Please see attached document. The following is a discussion of the vector calculations of Coulomb's law. If you indeed want to relate this to a time scale, then in stead of using static r values in your calculations, you make them time-dependent variables.
Coulombs Law - Explain the ...
Coulombs Law - Explain the Electromagnetic Force on Particles in relation to their x and y axis, related to a time scale - explanation and references.