Suppose we have a conservative vector field on a plane. Suppose also that we have a closed curve C on that plane. Then we have:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_C \mathbf{F}\cdot d\mathbf{r} = 0 [/tex]

The line integral around C is zero becauseFis conservative. Here is what I don't understand:

If you have one or more singularities (points at whichFis undefined) within the area bound by C then the line integral around C is no longer zero! How can this be?

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# Vector calculus

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