Flux of Electric field through sphere

[Tesla In Person]

Homework Statement

What is the flux of electric field through sphere with charges inside and outside of the sphere?

Relevant Equations

Electric field flux = Q/ e0

My attempt: We have 3 charges inside 2 +ve and 1 -ve so i just added them up. 4 + 5 +(-7) = 2q
Then there is a -5q charge outside the sphere. I did 2q + (-5q)= -3q . The electric field flux formula is Flux= q/ E0 . So i got -3q/E0 which is obviously wrong : ) . After quick googling , I discovered that the electric flux through a sphere is only dependent on charges enclosed by the sphere , charges outside don't affect electric flux through sphere. Is it correct and why it is the case? I am not familiar with Gauss' law so how do i get started. Thank you

 

[Orodruin]

After quick googling , I discovered that the electric flux through a sphere is only dependent on charges enclosed by the sphere , charges outside don't affect electric flux through sphere. Is it correct and why it is the case?

That is Gauss’ law.

 

[kuruman]

The sources of electric flux are charges. Think of them as sources (positive) and sinks (negative) of water. If a closed surfaces encloses source, water comes out of the surface at every point on it. Likewise, if a sink is enclosed, water goes into the surface at every point on it. If you have a combination of sources and sinks you need to add all the positives and negatives and see what the net is.

Now if a source is outside the surface and there are no sources or sinks enclosed by the surface, what goes into it through the side closer to the source must come out the other side. You put all this together and you have an intuitive understanding of Gauss's law.