Uniform charged sphere with hole?

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Homework Help Overview

The discussion revolves around the electrostatics of a uniformly charged sphere with a hole removed from it. Participants are exploring the implications of this modification on the application of Gauss's law and the potential need for superposition in calculating the electric field.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are considering whether Gauss's law is applicable in this scenario or if superposition is necessary. There are discussions about using the divergence theorem and the concept of an oppositely charged sphere to maintain electrostatic conditions. Suggestions include calculating the electric field for both the original charge distribution and the field produced by the hole.

Discussion Status

The discussion is active, with participants sharing various approaches to the problem. Some have suggested a method involving the calculation of electric fields from both the original sphere and an oppositely charged sphere to find a combined result. There is recognition of overlapping suggestions among participants.

Contextual Notes

Participants are navigating the complexities of applying electrostatic principles to a modified charge distribution, with specific attention to the assumptions regarding charge density and the configuration of the sphere.

philipc
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Lets say I have a sphere of uniform charge, and a hole was removed any where within the sphere, would Gauss law be usless and I would have to go with superpostion? And I'm wondering how to set the integral in either case.
Thanks
Philip
 
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many times the divergence teorem is hard to apply, then you can try to solve that thinking about the hole has a charge opposite to the complete sphere in order to maintain the electrostatic condition.
 
If you're trying to calculate the electric field in the case of the sphere "with a hole" in it then I recommend (a) calculate the field for the original charge distribution, (b) calculate the electric field produced by an oppositely charged sphere where the hole is and then (c) adding the results of (a) and (b).
 
Oh, sorry, I see Diego essentially made the same suggestion!
 
Thanks, let's see if I'm thinking right here? First I find the efield at the point as though there was no hole. 2) I find the efield of the point do to the smaller sphere using a -charge density. 3) I sum the two efields together to get final results?
Again thanks for your help
Philip
 

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