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Parametrize sphere for Stoke's Thm

  1. Dec 19, 2008 #1
    1. The problem statement, all variables and given/known data

    compute the flux of [tex]\stackrel{\rightarrow}{F} = <x,y,z>[/tex] through the sphere [tex]x^{2} + y^{2} + z^{2} = 1[/tex]

    2. Relevant equations

    [tex]\int\int_{S}Curl(\stackrel{\rightarrow}{F})\bullet ds = \int_{C}\stackrel{\rightarrow}{F}\bullet d\vec{r}[/tex]

    3. The attempt at a solution

    I am having trouble parametrizing the surface S (the sphere of radius 1). I know I have to find a normal vector for the surface (which I know intuitivley is <x,y,z>) but I dont know how to get there if I have a different problem that is not so easy to see.

    I tried parametrizing it in Spherical cordinates using two angles [tex](\phi, \vartheta[/tex]. Then I get for parametrzed equation

    [tex]x = sin(\phi)cos(\vartheta)[/tex]
    [tex]y = sin(\phi)sin(\vartheta)[/tex]
    [tex]z = cos(\phi)[/tex]

    which gives the Normal vector as

    [tex]n = < sin^{2}(\phi)cos(\vartheta), -sin^{2}(\phi)sin(\vartheta), cos(\phi)sin(\phi) >[/tex]

    This isnt right obviously...
    How am I suposed to parametrize a function in such as the ball???

  2. jcsd
  3. Dec 19, 2008 #2
    OK I found out what I needed...I was actualy mostly correct, aside from small computation errors :) Thanks anyway though
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