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:
- $\ds \int_O^A \mathbf F \cdot \d \mathbf l$
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $3$. Line and Surface Integrals