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Math Help - Flux of vector field through a surface.

  1. #1
    Ant
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    Flux of vector field through a surface.

    I'm I'm calculating the flux of

    v = (y, x)

    upwards across the upper half of the unit sphere. (sphere such that z >= 0)

    Is there two possible ways of going about this:

    Find N = ( - (partial derivative function wrt x) , - (particial derivative wrt y, 1, )

    the integrate v dot N with respect to x and y with the following limits:
     x \in  [-1, 2]
     y  \in   [ -\sqrt{1 - x^2}, \sqrt{1 - x^2}

    OR

    Parameterize S using spherical polar coordinates   \theta ,    \phi

    Find N as the cross product between the partial derivative wrt theta and phi.

    Then integrate v dot N with respect to theta and phi with the following limits:

     \phi  \in  [0, 2\pi ]
     \theta  \in [0, 2/\pi ]

    I THINK this is correct but I'm a little confused because in the first case I integral with limts corresponding to a unit circle in R2 but in the second case it seems like my limits are drawing out the actual unit sphere?

    Sorry for the lack of LateX I tried but failed to make it work!!

    Anyhelp really appreciated!
    Last edited by Ant; May 8th 2011 at 04:21 AM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Ant View Post
    Sorry for the lack of LateX I tried but failed to make it work!!
    Check out the general announcement near the top of any forum or search page. Use [tex] tags instead of [tex] for now.

    -Dan
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