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

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SUMMARY

The total electric flux through a spherical Gaussian surface with radius R/2, concentric to a uniformly charged insulating sphere of radius R, is calculated using Gauss' Law. The relevant equations include the volume of the sphere, Vsphere = (4∏R^3)/3, and the surface area, Asphere = 4∏R^2. The flux is determined to be Q/8ε0, where Q is the total charge enclosed within the Gaussian surface and ε0 is the permittivity of free space. This result is confirmed as correct based on the application of Gauss' Law.

PREREQUISITES
  • Understanding of Gauss' Law in electrostatics
  • Familiarity with the concepts of electric flux and charge distribution
  • Knowledge of the equations for the volume and surface area of a sphere
  • Basic principles of electrostatics and permittivity
NEXT STEPS
  • Study the derivation and applications of Gauss' Law in various geometries
  • Explore examples of electric flux calculations in different charge distributions
  • Learn about the implications of permittivity in electrostatics
  • Investigate the relationship between electric field strength and flux through surfaces
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Students studying electromagnetism, physics educators, and anyone interested in understanding electric flux and Gauss' Law applications in electrostatics.

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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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