Electric potential and potential energy

Electric potential energy, like gravitational potential energy, belongs to a specific charge sitting at a specific location — it is the work it took to bring that charge there, and it depends on how much charge you brought. Electric potential is different: it strips the "how much charge" out and leaves only the property of the location itself, potential energy per unit charge, V = U/q. A point near a fixed source charge has one definite potential whether you ever place a test charge there or not, exactly as a hillside has a definite steepness whether or not a ball happens to be rolling down it.

This is why the two quantities have different units — potential in volts (joules per coulomb), potential energy in joules — and why they cannot be used interchangeably. Once you know the potential at a point, finding the potential energy of any particular charge placed there is one multiplication: U = qV. A 2 C charge at a 5 V point has 10 J of potential energy; a 4 C charge at the same point would have 20 J, because potential energy scales with the charge you bring while the potential of the point does not change at all — the source charge, not the test charge, is what sets it.

Potential is what makes circuit analysis practical, because a battery's rating in volts is exactly this quantity: the potential difference it maintains between its terminals, independent of what current happens to be flowing. Voltage differences drive current the way height differences drive water downhill, and "high potential" and "low potential" are the electrical equivalent of "uphill" and "downhill" — a positive charge accelerates from high potential toward low, releasing potential energy as it goes.