Contour Integral/Examples/Work Done

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Example of Contour Integral

Let $\mathbf F$ be a force acting as a point-function giving rise to a vector field $\mathbf V$.

Let $OA$ be a contour in $\mathbf V$ along which a particle $P$ is moved by $\mathbf F$.

Let $\d \mathbf l$ be a small element of length of $OA$ at $P$.

Then the work done by $\mathbf F$ moving $P$ from $O$ to $A$ is given by the contour integral:

$\ds \int_O^A \mathbf F \cdot \d \mathbf l$


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