Potential Energy for Point Charges

When two objects interact you can look at the force they exert on one another or you can look at their potential energy.

For two masses m and M separated by a distance r the gravitational potential energy is:

Ug =
– G m M
r

Similarly, for two charges q and Q seperated by a distance r the electrostatic potential energy:

Ue =
k q Q
r

For both masses and charges the potential energy is zero when they are infinitely far apart.

What really matters is how the potential energy changes when masses or charges move relative to one another.