Definition:Conservative Vector Field/Definition 1

Definition
Let $R$ be a region of space.

Let $\mathbf V$ be a vector field acting over $R$. $\mathbf V$ is a conservative (vector) field the contour integral over $\mathbf V$ around every simple closed contour is zero:


 * $\ds \oint \mathbf V \cdot \d \mathbf l = 0$

Also see

 * Equivalence of Definitions of Conservative Vector Field