# Finalize Potential and Force

Let be two points. The potential between these two points is

More prescisely, the potential actually is a function of :

(Only depend on the distance but not direction, even function).

**The force applied to is .**

**The force applied to is .**

**Highlight:**

Physical interpretion: easy! The direction of the force points to the negtive gradient!

The gradient of with respect to means: if can move ( can’t move), moving along the force direction, the potatial decrease the fastest.

Mathematically, it is easy to see . Hence .

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EDIT:

The force and potential are only functions of . More specifically, the potential is a function of . So it can be usually seen that the force and potential are written as

and

where .

And because and

**The force applied to is .**

**The force applied to is $latex F_{x_{ji}}=- F_{x_{ij}}$.**