Calculating the net electric flux

[anonymousphys]

Homework Statement

When calculating the net electric flux, we use the equation EA=electric flux. If there are multiple charges in different closed surfaces, do we use the net electric field multiplied by the area for each closed surface to solve the electric flux for a single closed object? How does this work mathematically in terms of the proof for electric flux (more specifically the one where we use a sphere to derive the equation for electric flux? (phi=Q/E)). In other words, how do we prove mathematically that the net electric flux in one closed surface is only due to the net charge placed in the closed surface?

Homework Equations

EA=electric flux
phi=(net charge)/(constant)

The Attempt at a Solution

I believe the answer to the first question is yes?

Sorry if many questions were mixed together, I had many questions on my mind.
Thanks for any replies.

 

[tiny-tim]

How does this work mathematically in terms of the proof for electric flux (more specifically the one where we use a sphere to derive the equation for electric flux? (phi=Q/E)). In other words, how do we prove mathematically that the net electric flux in one closed surface is only due to the net charge placed in the closed surface?

Hi anonymousphys!

From Gauss' theorem (the divergence theorem), the flux through a closed surface equals the integral (over the interior) of the divergence of the field …

and the divergence will be zero (∇.E = 0) for the field produced by any charge outside the surface.