What is the Charge Distribution on Concentric Spherical Shells?

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SUMMARY

The discussion centers on the charge distribution of two concentric conducting spherical shells, where the inner shell has a net charge of -8 C and contains a 2 C point charge. Applying Gauss's Law, the charge on the inner radius of the inner shell is determined to be -2 C, while the outer radius of the inner shell holds -6 C. The outer shell's inner radius has a charge of 0 C, and the outer radius carries a charge of +6 C, resulting from the total charge inside the outer shell being -6 C.

PREREQUISITES
  • Understanding of Gauss's Law
  • Knowledge of electrostatics and charge distribution
  • Familiarity with conducting spherical shells
  • Basic principles of electric fields in conductors
NEXT STEPS
  • Study Gauss's Law applications in electrostatics
  • Explore charge distribution in conductors
  • Learn about electric field calculations for spherical geometries
  • Investigate the effects of point charges on surrounding conductors
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Students studying electrostatics, physics educators, and anyone interested in understanding charge distribution in conducting spherical shells.

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Homework Statement



You have two concentric conducting sherical shells. the net charge in the inner shell is -8 C and the outer shell is neutral. In the inner hollow is placed a 2C point charge. Using Gauss's Law, find the charge on all 4 surfaces of the shells.

Homework Equations



Econductor = 0

The Attempt at a Solution


Inner radius of inner shell: -2C
Outer radius of inner shell: -6C
Inner radius of outer shell: 0
Outer radius of outer shell: 0

Not sure how to use Gauss's law here, or if the answers for the outer shell are right.
 
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Try envisioning a Gaussian sphere that lies outside the inner radius of the inner sphere but inside the outer radius. Do the same for the outer sphere.
 
I think this means the inner shell answers are correct, but not the outer. Is the outer shell going to have a -8 charge on the inner radius and a positive 8 charge on the outer?
 
Not -8. Think about how much charge there is inside the outer shell.
 
Oh! There is -6C inside the outer shell. So 6C on the inner and -6 on the outer.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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