Divergence and Flux

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

hi demoz! welcome to pf!

Quote by 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?

across any closed surface, yes

otherwise, no

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demoz	Divergence and Flux Tweet 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?