Conservative Force

Definition: Conservative Force

A force $\mathbf{F}$ is conservative if it satisfies the following criteria:

1. The work done by $\mathbf{F}$ depends only on the start and end positions of the point mass it acts on, i.e. it is path-independent.

2. The work done by $\mathbf{F}$ along any closed path $\mathcal{O}$ is $0$.

$${\oint }_{\mathcal{O}}\mathbf{F}\cdot \mathrm{dr}=0$$

3. The force $\mathbf{F}$ is a gradient field.

NOTE

If $\mathbf{F}$ satisfies at least one of these criteria, then it satisfies all of them.