Flux integral is equal to zero

[mathwizeguy]

Homework Statement

If s is a unit sphere, centered on the origin and oriented outward, and the flux integral is eual to zero, does F=0?

Homework Equations

The Attempt at a Solution

 

[ystael]

Not necessarily. Think for a bit and you should be able to come up with some simple examples of vector fields where the flux through different parts cancels out when you integrate it over the whole surface.