Coming from a Chemistry background, we seem to flippantly explain away chemical phenomena using "Coulomb's Law" but are often specifically mentioning the equation for electrostatic potential energy due to their similarity. The explanatory power for us is about the same, but one is an inverse-square law and the other just proportional to 1/r. Why is this? I recognize one is describing a force, and the other an energy, but I'm having difficulty finding any way to mathematically discover why there's the difference in denominator beyond just hand-waving or beyond stepping quite out of my knowledge set to derive it myself hah. Also, is it appropriate for us as Chemistry instructors to use the terms interchangeably when explaining phenomena, or is this bad bad practice? Thanks much!