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Closed integral

  1. Jul 24, 2013 #1
    in a text a read that

    "[tex] \oint \nabla A \cdot dl = 2 \pi n [/tex]

    wich implies that the gradient of A has a pole singularity"

    why there is a singularity?

    I thing that this is a contidion to integral is nonzero but ¿what is the theorem used?
     
  2. jcsd
  3. Jul 24, 2013 #2

    lurflurf

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    by stokes theorem

    $$\oint \! \bf{\nabla A} \cdot \mathrm{dl}=\iint \! \bf{\nabla \times (\nabla A)} \cdot \mathrm{ds}$$

    clearly the curl of the gradient is zero so the integral is only nonzero if there is a singularity.
     
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