\begin{definition}[Definition:Curl Operator/Physical Interpretation]
Let $\mathbf V$ be a vector field acting over a region of space $R$.
Let a small vector area $\mathbf a$ of any shape be placed at an arbitrary point $P$ in $R$.
Let the line integral $L$ be computed around the boundary edge of $A$.
Then there will be an angle of direction of $\mathbf a$ to the direction of $\mathbf V$ for which $L$ is a maximum.
The '''curl''' of $\mathbf V$ at $P$ is defined as the vector:
:whose magnitude is the amount of this maximum $L$ per unit area
:whose direction is the direction of $\mathbf a$ at this maximum.
\end{definition}