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Math Help - integration of a 2-form over en sphere

  1. #1
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    integration of a 2-form over en sphere

    f=\frac{E}{4\pi}(\frac{x}{(x^2+y^2+z^2)^{3/2}}dy\wedge dz+\frac{y}{(x^2+y^2+z^2)^{3/2}}dz\wedge dx+\frac{x}{(x^2+y^2+z^2)^{3/2}}dx\wedge dy)

    over a sphere x^2+y^2+z^2 \ge \mathbb{R}^3
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by rayman View Post
    over a sphere x^2+y^2+z^2 \ge \mathbb{R}^3

    That inequality has no sense.
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    Quote Originally Posted by FernandoRevilla View Post
    That inequality has no sense.
    of course it should be  x^2+y^2+z^2\ge R^2
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    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by rayman View Post
    of course it should be  x^2+y^2+z^2\ge R^2

    I suppose you mean the sphere S\equiv x^2+y^2+z^2=R^2. In such case, apply the Divergence Theorem to V-V_r where 0<r<R . That is,

    \iint_Sw+\iint_{S_r}w=\iiint_{V-V_r}dw=0

    So,

    \iint_Sw=-\iint_{S_r}w
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  5. #5
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    Thank you for your reply.

    actually it is supposed to be like I wrote earlier  x^2+y^2+z^2\ge R^2 that is actually what my teacher says. I will apply Gauss-Otrogradski theorem to it and she what happens.
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