The vector field [itex]\vec{F} = <\frac{-y}{x^2 + y^2},\frac{x}{x^2 + y^2},0>[/itex] has a zero curl, which means its circulation is zero. However(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int \vec{F}.d\vec{s}[/itex] around a unit circle on the xy plane is equal to [itex](+/-)2\pi[/itex] and not zero

Is it because F is undefined at (0,0)? No, because Stoke's theorem allows me to choose an arbitrary surface not including the origin(0, 0, 0)?

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# Zero curl but nonzero circulation

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