Uniform charged sphere with hole?

In summary, the conversation discusses the application of Gauss law in the case of a sphere with a hole and how to set up the integral. It is suggested to solve this problem by considering the hole as a charge with opposite polarity to the rest of the sphere. Another suggestion is to calculate the electric field for the original charge distribution and then add the field produced by the hole using an opposite charge. The conversation concludes with Philip confirming his understanding of the process and thanking for the help.
  • #1
philipc
57
0
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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  • #2
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.
 
  • #3
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).
 
  • #4
Oh, sorry, I see Diego essentially made the same suggestion!
 
  • #5
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
 

1. What is a uniform charged sphere with hole?

A uniform charged sphere with hole is a physical system that consists of a spherical shell with a hole in the center, surrounded by a uniform distribution of electric charge.

2. How is the charge distributed in a uniform charged sphere with hole?

The charge in a uniform charged sphere with hole is evenly distributed on the surface of the sphere, with no charge present inside the hole.

3. What is the electric field inside a uniform charged sphere with hole?

Inside the hole, the electric field is zero since there is no charge present. Outside the sphere, the electric field is the same as that of a point charge located at the center of the sphere.

4. How does the electric potential vary in a uniform charged sphere with hole?

The electric potential inside the hole is constant and equal to zero, while outside the sphere, it decreases as the distance from the center increases, following the same pattern as a point charge.

5. What is the total charge of a uniform charged sphere with hole?

The total charge of a uniform charged sphere with hole is the same as the charge on the surface of the sphere, since there is no charge inside the hole.

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