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# Gauss Theorem watch

1. 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?
2. (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.
3. (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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