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)?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Zero curl but nonzero circulation

**Physics Forums | Science Articles, Homework Help, Discussion**