Why is an electric force conservative?
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:
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.
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.