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Let $F(x,y,z)=(6x,-2y,5z)$ a vector field and $S$ the surface of the sphere centered at $(1,0,1)$ e radius $5$. Find the flux of $F$ across the surface $S$.

I want to use the Gauss theorem, and my problem is when i use spherical coordinates how can i found the bounds for $\rho$, $\psi$ if the sphere is not centered at the origin.

Thank you

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  • $\begingroup$ the integral of a "constant" over a ball is equal to the product of that constant and the volume of ball. $\endgroup$
    – achille hui
    Jun 22, 2015 at 8:52

1 Answer 1

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Hint.

Why don't you use integration by substitution using a translation in order to reduce the problem to one where the sphere is centered at the origin?

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