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

AI Thread Summary
The discussion revolves around calculating the total electric flux through a spherical Gaussian surface with radius R/2 surrounding a uniformly charged insulating sphere of radius R. Using Gauss' Law, the participant attempts to derive the flux expression and arrives at Q/8ε0, expressing uncertainty about its accuracy. The conversation emphasizes the importance of understanding the relationship between charge distribution and flux through Gaussian surfaces. Participants clarify the application of Gauss' Law, confirming that the flux calculation is indeed correct. This highlights the significance of grasping the underlying principles of electrostatics in problem-solving.
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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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