Flux of F When DivF=0 in 3D Surfaces

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SUMMARY

If F is a well-defined vector field and divF=0, the flux of F across any closed surface in 3D is definitively zero. However, this does not imply that the flux across flat surfaces or planes is also zero. The divergence theorem confirms that divF=0 leads to a zero integral over closed surfaces, but the behavior of flux across non-closed surfaces varies and cannot be generalized.

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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?
 
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welcome to pf!

hi demoz! welcome to pf! :smile:
demoz said:
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 :wink:​
 

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