# 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.

• Potential of a negative charge is increasing as it gets attracted. potential energy however is getting smaller, as you multiply potential by Nov 21, 2021 at 4:03

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.