Hey all. I have a question regarding potential vs. potential energy. Basically, from what I can tell, the potential energy is a property of the system as a whole (it has a single value in any given situation) while the potential is a property of each specific point in space. Would this be like saying that the potential and any point is equal to the potential energy the system WOULD have if you placed a charge of charge q at that point? Why then do we deal with both quantities... it seems to me like the potential is really just potential energy except that we are dividing out the charge of a "hypothetical point charge" that we could have added to the system, but then take out to make the math simpler. Is this an ok way to think about it-- that the potential energy WOULD be what the potential is multiplied by a charge placed at that point... that would be a seemingly redundant definition, though. Thanks in advance for clarification!