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What is the total flux flowing through a spherical Gaussian surface?

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Homework Statement


Consider a uniformly charged sphere (an insulating sphere of radius R,) and a spherical Gaussian surface with radius R/2 concentric to the sphere. What is the total flux flowing through the Gaussian surface?

Homework Equations


Vsphere= (4∏R^3)/3
Asphere= 4∏R^2

Gauss' Law:
Flux = ρVinside/ε0 = PHI = QVinside/Voutside


The Attempt at a Solution


Ok, so I am familiarizing myself with these concepts, and I can't find a concrete example such as this one in the text. I'm pretty sure that simply by relating the equations for volume by Gauss' Law above can give me a compact expression for the Flux. BUT I'm not sure.
I gave it a shot by using the eqn above and simplified this expression to Q/8ε0. I am skeptical of its correctness. Can someone explain if I'm doing this correctly, and if so qualitatively describe why? Thanks! First post!
 
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