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Math Help - flux of a sphere

  1. #1
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    flux of a sphere

    calculate the flux of F = (z,4,-xy) out of the sphere x^2 + y^2 +z^2 = 4

    cheers
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  2. #2
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    Quote Originally Posted by hugolovesmaths View Post
    calculate the flux of F = (z,4,-xy) out of the sphere x^2 + y^2 +z^2 = 4

    cheers
    Oh blast! I wrote out a whole long treatise on how to find the vector differential of surface area and then realized it is far easire to use the "divergence theorem".

    That says that \oint\oint \vec{F}\cdot d\vec{S}= \int\int\int \nabla\cdot\vec{F} dV.

    And, for \vec{F}= z\vec{i}+ 4\vec{j}- xy\vec{k}, \nabla\cdot\vec{F}= \vec{0}!
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