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    The question asks to evaluate the surface integral of a vector field over the surface of a unit sphere, and to verify it using the volume integral via the gauss theorem. This is my working:



    ...I tried. Is it catastrophically wrong or have I just done silly mistakes?
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    (Original post by Plagioclase)
    The question asks to evaluate the surface integral of a vector field over the surface of a unit sphere, and to verify it using the volume integral via the gauss theorem. This is my working:


    Hi
    ...I tried. Is it catastrophically wrong or have I just done silly mistakes?
    I'm not sure where your pi / 2 sin phi term has come from in the 2nd line of integration. I think you have 1 error there.

    When you try to solve by Gauss, the r^2 part of the volume disappears erroneously. This makes your answer here 3 times too big.
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    (Original post by DFranklin)
    I'm not sure where your pi / 2 sin phi term has come from in the 2nd line of integration. I think you have 1 error there.

    When you try to solve by Gauss, the r^2 part of the volume disappears erroneously. This makes your answer here 3 times too big.
    Awesome, thank you so much!
 
 
 
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