# Flux through sphere symmetry?

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?

• Did you check by using the divergence theorem? It should tell you pretty quickly whether you are correct or not. The example in the Wiki page pretty much does your question for you. – Mattos Feb 14 at 0:58
• the divergence is 1+0-1= 0 conveniently? So the integral of divergence is 0? (we are integrating with limits) Is this a correct line of reasoning – Dis-integrating Feb 14 at 1:29
• Yes, the divergence theorem shows the integral to equal $0$. – Mattos Feb 14 at 1:31