Category:Definitions/Conservative Vector Fields

This category contains definitions related to Conservative Vector Fields.
Related results can be found in Category:Conservative Vector Fields.

Let $R$ be a region of space.

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

Definition 1

$\mathbf V$ is a conservative vector field if and only if the contour integral over $\mathbf V$ around every simple closed contour is zero:

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

Definition 2

$\mathbf V$ is a conservative vector field if and only if its curl is everywhere zero:

$\curl \mathbf V = \bszero$