1. flux of a sphere

calculate the flux of F = (z,4,-xy) out of the sphere x^2 + y^2 +z^2 = 4

cheers

2. Originally Posted by hugolovesmaths
calculate the flux of F = (z,4,-xy) out of the sphere x^2 + y^2 +z^2 = 4

cheers
Oh blast! I wrote out a whole long treatise on how to find the vector differential of surface area and then realized it is far easire to use the "divergence theorem".

That says that $\oint\oint \vec{F}\cdot d\vec{S}= \int\int\int \nabla\cdot\vec{F} dV$.

And, for $\vec{F}= z\vec{i}+ 4\vec{j}- xy\vec{k}$, $\nabla\cdot\vec{F}= \vec{0}$!