Circulation

of a vector field $\mathbf{a}(\mathbf{r})$ along a closed curve $L$

The integral

$${\oint }_L\mathbf{a}d\mathbf{r}.$$

In coordinate form the circulation is equal to

$$\underset{L}{\int }(a_{x}dx+a_{y}dy+a_{z}dz).$$

The work performed by the forces of the field $\mathbf{a}(\mathbf{r})$ in displacing a test body (of unit mass, charge, etc.) along $L$ is equal to the circulation of the field along $L$. See Stokes theorem.

Comments[edit]

This notion is also called a line integral (of a vector field) along a closed curve.