Work done and potential energy of electrostatic interactions

3 Work done and potential energy of electrostatic interactions 

If the external force pushing or pulling at the charges as they are repelled or attracted to each other is very nearly equal and opposite to the electrostatic force between the charges, then all the changes in position can take place very, very slowly, and so the kinetic energy will remain effectively constant. 

Hence to obtain an expression for the potential energy of electrostatic interactions between the two charges requires that an expression for the work done in bringing the two charges from a 

Force between charges Equal and opposite external force 

But to evaluate the work done, w, the force which is required is the external force which is either pushing the charges together or pulling them apart depending on whether there is repulsion or attraction between the charges. This force will be equal and opposite to the force of interaction. 

---