Flux of F When DivF=0 in 3D Surfaces

[demoz]

If F is a well defined vector field and divF=0 then does that mean the flux of F across any surface in 3D would also be 0?

I know that in divergence theorem, divF=0 automatically implies that the integral will be 0 but what about across flat surfaces and planes?

 

[tiny-tim]

welcome to pf!

hi demoz! welcome to pf!

If F is a well defined vector field and divF=0 then does that mean the flux of F across any surface in 3D would also be 0?

across any closed surface, yes

otherwise, no ​