Calculating Flux Through a Gaussian Spherical Shell Inside a Charged Sphere

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SUMMARY

The discussion focuses on calculating the electric flux through a Gaussian spherical shell of radius R/2, which is located inside a uniformly charged insulating sphere of radius R with a volume charge density ρ. The correct approach involves using the formula for electric flux, φ = qenclosed/ε₀, where qenclosed is derived from the volume charge density multiplied by the volume of the Gaussian shell. The initial calculation attempted by the user was incorrect, but they successfully resolved the issue by correctly applying the principles of Gauss's Law.

PREREQUISITES
  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric flux concepts
  • Knowledge of volume charge density and its implications
  • Basic calculus for volume calculations of spheres
NEXT STEPS
  • Review Gauss's Law and its applications in electrostatics
  • Study the concept of electric flux in different geometries
  • Explore the implications of volume charge density in electric fields
  • Practice problems involving Gaussian surfaces and charge distributions
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone looking to deepen their understanding of electric fields and flux calculations in charged systems.

Gee Wiz
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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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