Gauss's Law and electric flux of a surface

[Keithkent09]

Four closed surfaces, S1 through S4, together with the charges -2Q, Q, and -Q are sketched in the figure below. (The colored lines are the intersections of the surfaces with the page.) Find the electric flux through each surface. (Use Q for the charge Q and epsilon_0 for 0.)
(Picture Attached)

2.
Electric Flux= the integral of EdA=q/epsilon_0


3.
All that I could think to do was set q=the charge of the inside of the desired surface. I was not sure how I could quantitatively define how the different charges within the surfaces affected each other.

 

[dacruick]

Gauss` law is your best friend. the flux through a surface will only be non zero if there is a charge inside that surface. think about putting an imaginary sphere in the middle of a river. All the water that runs into the sphere also runs out of it. Having a charge inside the surface is like putting a sprinkler inside your imaginary sphere. Now the amount of water in is 0, and the amount of water out is this analogy`s version of flux.

So any surface with no charge inside, has 0 flux.

This principle is displayed simply in your equations for flux. where flux is = to
charge enclosed / epsilon naught.

So your flux for the red surface with Q and -2Q, it will have a flux of -Q/epsilon naught