Consider the equations for electric potential energy:
and gravitational potential energy:
In the case of GPE, the potential energy increases as the distance between the two objects increases. This makes sense (to me), as the greater distance between the Earth and an object for example, the greater distance there is to fall and thus more kinetic energy to build up. No problem.
With electric potential energy however, distance has the opposite effect, with potential energy decreasing as the distance between the two charged objects increases.
In the situation of two oppositely charged particles, why do we not consider the charges to be 'falling' towards each other like in the gravitational example, and thus the potential energy will be less the closer together they are when the potential is measured?
GPE and EPE are constantly being used as analogous examples, but the equations used to calculate them don't seem to be analogous at all to me, at least in the case where the charges are attracted and move towards each other.
The Attempt at a Solution