Net flux of arbitrary closed surface when the field is constant everywhere, should be zero. ( while the source of the field isn't inside of the volume closed by the surface )

I somehow can understand why is that true, bu what I need is a mathematical proof of that sentence

  • $\begingroup$ It sounds as if you're asking for a proof of the divergence theorem, in which case a quick Google will find you any number of articles discussing this. $\endgroup$ – John Rennie Aug 2 '16 at 7:03
  • $\begingroup$ Just Google it! $\endgroup$ – user114592 Aug 2 '16 at 12:37
  • 3
    $\begingroup$ I'm voting to close this question as off-topic because of insufficient research effort. $\endgroup$ – sammy gerbil Aug 2 '16 at 15:00

Flux means integral of dot product of a vector field with an oriented surface. If the field (vector field) is constant, that means it has zero divergence. So, the divergence theorem is the mathematical support for the integrated flux through a closed surface vanishing.

See https://en.wikipedia.org/wiki/Divergence_theorem

A 'source' of a vector field is a way of describing divergence, so 'no source inside' is a claim that divergence is zero in the volume.

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