A question about conducting sphere using Gauss's Law

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SUMMARY

The discussion centers on calculating the surface charge densities of a conducting spherical shell with a positive point charge Q at its center and a total shell charge of -3Q. The inner surface of the shell acquires a charge of -Q, while the outer surface has a charge of -2Q. The relevant equation used is EA = Q enclosed / ε0, where E is the electric field, A is the area, and ε0 is the permittivity of free space. The user seeks clarification on determining the area of the spherical surfaces defined by the inner radius a and outer radius b.

PREREQUISITES
  • Understanding of Gauss's Law and its application in electrostatics
  • Familiarity with concepts of electric field and charge distribution
  • Knowledge of spherical geometry for calculating surface areas
  • Basic principles of electrostatics, including charge conservation
NEXT STEPS
  • Learn how to apply Gauss's Law to different charge configurations
  • Study the derivation and implications of surface charge density formulas
  • Explore the calculation of surface area for spherical geometries
  • Investigate the effects of charge distribution on electric fields in conductors
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone studying electrostatics, particularly those focusing on charge distributions in conducting materials.

ehabmozart
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Homework Statement



A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is -3Q, and it is insulated form it surroundings. What is the surface charge density on the inner surface of the conducting shell.? What is the surface charge density on the outer surface?

Homework Equations



EA= Q enclosed / ε0

The Attempt at a Solution



I know that since there is a point charge, this will change up the configuration a bit making the inner surface having -Q and outer surface to have -2Q charge enclosed. I have problems in determining the area. I don't know when does the inner end and when does the outer surface begin. Is it half way?? What would be the area then?
 
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The radii of the inner and outer surfaces are given, a and b. Do you know how to calculate the area of a spherical surface from the radius?

ehild
 

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