# Why is an electric force conservative?

##### 1 Answer

The work done by the electric force along a path starting and ending at the same point

#### Explanation:

We are given:

Force is conservative if work done along a path that starts and ends at the same point is 0.

Work is given as:

where

Let's make our path start and end at the same point

We have shown that the work done by the electric force along a path starting and ending at the same point is 0. Hence, the electric force is conservative.

=======================EDIT=======================

There are three equivalent statements for showing a force is conservative:

- (1) The cross product of the force vector is 0:

- (2) The work done by the force vector along a path that starts and ends at the same point is 0:

- (3) A force vector is the negative gradient of the potential:

I demonstrated (2) in the answer given.