Calculating Flux Through a Gaussian Spherical Shell Inside a Charged Sphere

AI Thread Summary
The discussion focuses on calculating the electric flux through a Gaussian spherical shell located inside a uniformly charged insulating sphere. The volume charge density is given as ρ, and the radius of the Gaussian shell is R/2. The initial approach involved calculating the enclosed charge using the formula for volume and dividing by Eo, but this method did not yield the correct result initially. Ultimately, the user resolved the issue and arrived at the correct calculation for the flux. The key takeaway is the importance of correctly applying the charge density and volume relationships in Gauss's law.
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Homework Statement


An insulating sphere of radius R has positive charge uniformly distributed throughout its volume. The volume charge density (i.e., the charge per volume) is ρ.

What is the flux through a Gaussian spherical shell of radius R/2 that is totally contained inside the charged sphere and centered a distance R/2 from the center of the charged sphere, as shown by the dashed sphere in the diagram below?

Homework Equations


flux=(qenclosed/Eo)

The Attempt at a Solution


I initially took ρ times the volume enclosed (4/3)*∏*(r/2)^3 and then divided that by Eo. But it didn't give me the correct result
 
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nevermind. figured it out
 

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