Is the flux through a sphere centered at the origin of the vector field $\boldsymbol{F} = (-x,1,z)$ equal to $0$? If so, is there any simple symmetry which suggests it? I have done the calculation which yielded a very complicated integral but it turned out to be $0$ (I should hope). I just want to know if there is any easy way of seeing this?
2026-03-25 12:46:31.1774442791
Flux through sphere symmetry?
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