Charge must be present at a location in order for there to be electrical potential energy. Must charge also be present at a location for there to be electric potential?

Question

I know it's no but why?

Answer 1

Say you have an electron at the origin.

The electron has potential energy.

The space between the electron and infinity has no potential energy if it has no charge because potential energy is charge TIMES potential.

The empty space does have potential though because there is an E field throughout that space caused by the electron.

If you put a charge into that E field, it would have potential energy and positive or negative work would have to be done to get it there depending on the sign of the charge.

Answer 2

Electric potential exists if work must be done to bring a "test" charge there, no matter what that test charge is. Electric potential (V) depends upon the amount and proximity of other charges.

Electric potential energy is q*V. V (the electric potential) does not depend upon qhat q is.

Answer 3

I find it easier to view this from a mathematical standpoint:
electric potential = electrical PE/ charge
If the charge is 0, you have
electric potential = electrical PE/ 0
you cannot have a zero in the denominator.