Definition:Conservative Vector Field

Definition
Let $R$ be a region of space.

Let $\mathbf V$ be a vector field acting over $R$.

Then $\mathbf V$ is a conservative (vector) field the line integral over $\mathbf V$ around every simple closed contour is zero:


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

Also known as
A conservative field is also known in the literature as:


 * a scalar potential field (from its property that it is the gradient of some scalar field)


 * a non-curl field.

A vector in such a field is sometimes known as a lamellar vector.

Also see

 * Vector Field is Expressible as Gradient of Scalar Field iff Conservative