\begin{definition}[Definition:Conservative Vector Field/Definition 1]
Let $R$ be a region of space.
Let $\mathbf V$ be a vector field acting over $R$.
$\mathbf V$ is a '''conservative (vector) field''' {{iff}} the line integral over $\mathbf V$ around every simple closed contour is zero:
:$\ds \oint \mathbf V \cdot \d \mathbf l = 0$
\end{definition}