How Does the Electric Energy formula Depict Energy Between a Positive and Negative?

012anonymousx

This is probably a silly question.

The Electrical energy formula is this:
Ee = k(q1)(q2)/r

So lets say a positive and negative charge are directly next to each other.
Conceptually, there should be no potential energy there.
But the formula (r=0.00001m) suggests that it is huge.

On the other end, if two positive charges are far away from each other (r=1000), energy should be huge, but the formula suggests it gets smaller.

I appreciate all the help!

Whovian

Actually, it says it should be hugely negative, as q1q2 is negative. Bringing them apart (increasing r) should increase the potential energy, which makes sense, as it takes energy to move them apart. (Note that the concept of negative energy might seem counterintuitive at first, but, by gauge symmetry, the only thing we care about is the difference between two energies in a potential field.)

On the contrary, the energy should be tiny, as you have to pour in some energy to overcome the force repelling the charges.