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Line integral around a circle in polar coordinates

  1. May 28, 2013 #1
    I know that [itex]\oint_{C}\mathrm{d}\vec{l} = 0[/itex], for any closed curve C.
    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.
  2. jcsd
  3. May 28, 2013 #2


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  4. May 28, 2013 #3
    Thanks.. I appreciate it.
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