# If electric charges accelerate towards lower potential energies, why do opposite charges attract?

I know my logic must be wrong but I can't figure out why. I know that charges must accelerate towards lower potential energies simply because that's a general rule of nature. However, when you release a positive and negative charge close to each other, they will move towards each other, and the distance between will decrease causing the potential energy to increase (1/r^2 relationship). So aren't the two charges gaining potential energy? Does it have to do with the sign of the charges being different? I feel like that explanation doesn't fit entirely because it seems like the magnitude of the potential energy should not be increasing.

The potential energy between two oppositely charged particles goes like $-1/r$. First of all, the potential energy doesn't scale as $1/r^2$; you must have confused it with the force which is the gradient (spatial derivative) of the potential energy. Second of all, the potential energy of a bound state – a pair or collection of particles/objects that attracted each other – is negative.