I know that [itex]\oint_{C}\mathrm{d}\vec{l} = 0[/itex], for any closed curve C.(adsbygoogle = window.adsbygoogle || []).push({});

But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero.

Here is my approach : [itex]\oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi = 2\pi\hat{\phi} \neq 0[/itex]

Since the line element [itex]\mathrm{d}\vec{l}[itex] is pointing in the azimuthal direction.

Where do I make a mistake?

Thank you in advance.

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# Line integral around a circle in polar coordinates

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