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Homework Help: Stokes' theorem over a circular path

  1. Apr 20, 2005 #1
    I need complete assistance on this :-)

    Check the Stokes' theorem using the function [tex]\vec v =ay\hat x + bx\hat y[/tex]
    (a and b are constants) for the circular path of radius R, centered at the origin of the xy plane.

    As usual Stokes' theorem suggests:
    [tex]\int_s {(\nabla\times \vec v).d\vec a = \oint_p\vec v.d\vec r [/tex]

    How do you compute:
    1. the area element [tex]d\vec a[/tex]
    2. the line integral
    For the circular path in this case.

    Hints will do!
  2. jcsd
  3. Apr 20, 2005 #2


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    You can do everything in polar plane coordinates,or in rectangular cartesian.It's your choice.

    Make it.

  4. Apr 20, 2005 #3


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    You don't need the expression for the area element. Just compute the curl and you'll immediately see what the answer should be (draw a picture as well).
    Remember that you're at liberty to choose the surface that is bounded by the circle.

    For the line integral the parametrization x=Rcos t, y=Rsin t, 0<=t<=2pi will do.
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