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Stokes theorem

  1. May 13, 2009 #1
    use the stokes theorem to evaluate the surface integral [curl F dot dS] where
    F=(x^2+y^2; x; 2xyz)
    and S is an open surface x^2+y^2+z^2=a^2 for z>=0. So i guess its a hemisphere of radius a lying on x-y plane.
    I don't see however how to take F dot dr. What is this closed curve dr bounding this hemisphere? I guess we can take spherical polar coordinates, but still once i have x,y,z in terms of r,phi,theta i still don't know "dr" (just differentiate ?) and what will the limits of integration be? Can someone show me?
  2. jcsd
  3. May 13, 2009 #2


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    Gold Member

    The boundary of the surface is just the circle x² + y² = a² in the xy plane. Did you try drawing a picture?
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