Solid insultaing sphere electric field

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SUMMARY

A solid insulating sphere of radius R with a uniform charge density ρ generates an electric field inside the sphere at a radius of R/2. Using Gauss' Law, the electric field E can be expressed as E = (4ρR) / (3ε₀), where ε₀ is the permittivity of free space. The charge Q within the Gaussian surface is calculated by integrating the charge density over the volume of the sphere up to radius R/2. This approach confirms the application of Gauss' Law in electrostatics for spherical charge distributions.

PREREQUISITES
  • Understanding of Gauss' Law in electrostatics
  • Familiarity with electric field concepts
  • Knowledge of charge density and volume calculations
  • Basic calculus for integrating charge density
NEXT STEPS
  • Study the derivation of electric fields using Gauss' Law for different charge distributions
  • Learn about the concept of electric flux and its calculation
  • Explore the implications of charge density variations in electric fields
  • Investigate the relationship between electric fields and potential energy in electrostatics
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Physics students, electrical engineering students, and anyone studying electrostatics or electric field theory.

odyssey4001
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Homework Statement


A solid insulating sphere of radius R carries a charge per unit volume of p. Use Gauss' law to find an expression for the eletric field on a spherical surface of radius R/2 ie: inside the sphere.


Homework Equations


Gauss' Law = (Net Flux = Q / Eo)

Volume of a Sphere = (4/3)(pi)(R^3)


The Attempt at a Solution


I simply combined Gauss' Law and the volume of the sphere to get,

E = (4Q) / [(3)(pi)(Eo)((R/2)^3)]

That seems to easy though have I missed something?
 
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odyssey4001 said:
I simply combined Gauss' Law and the volume of the sphere to get,

E = (4Q) / [(3)(pi)(Eo)((R/2)^3)]
Not sure what you did here. What's Q? Express the charge within the gaussian surface in terms of ρ. How do you calculate the flux?
 

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