# Electric potential energy

Bassel
hi, please can anyone analyze the following sentence in terms of the formulas of electrostatic forces or Potential energy (assuming electrostatic force is directly proportional to potential energy)
statement: "When the force between two objects is attractive and decreases with distance, the lowest potential energy level for those objects is when they are the CLOSEST to each other."

## Answers and Replies

Mentor
assuming electrostatic force is directly proportional to potential energy
Force is proportional to the gradient of the potential energy. Actually, they are not just proportional, they are the same.

The attractive force alone is sufficient here - it is another way to say "potential is lower for a smaller separation".

I moved the thread to classical physics, as I don't see a relation to nuclear or particle physics.

d.arbitman
Let's draw an analogy with gravity. A tennis ball and the Earth are two objects that are attracted to each other and the force between them falls as 1/r2. When they are touching each other (i.e. the ball is on the ground) there is zero potential energy but at the same time there is some attractive force between them. When you move the tennis ball away from the earth, let's say you increase the distance by Δr, then the force decreases due to the 1/r2 relationship, but at the same time, it's potential energy increased.

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