# Circulation

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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

$$\int\limits _ { L } ( a _ {x} dx + a _ {y} dy + a _ {z} dz).$$

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.