Uniform charged sphere with hole?

philipc

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

diegojco

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.

Tide

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).

Tide

Oh, sorry, I see Diego essentially made the same suggestion!

philipc

Thanks, lets 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