Definition:Rotational Vector Field

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Let $R$ be a region of space.

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

Then $\mathbf V$ is a rotational vector field if and only if the curl of $\mathbf V$ is not everywhere zero:

$\curl \mathbf V \not \equiv \bszero$

That is, if and only if $\mathbf V$ is not conservative.

Also see