Electric Field using Gaus's Law

[benndamann33]

A uniformly charged spherical shell with surface charge density omega contains a circular hole in its surface. The radis of the hole is smalle compared with the radius of the sphere. What is the electric field at the center of the whole(Hint: the field within the whole is the suprposition of the field due to the original uncut sphere, plus the field due to a sphere the size of the hole with a uniform negative charge density -omega)

I don't undestand this because the electric field, if the sphere were solid, doesn't depend on the radius, it's just q/(epsilon_0). Any idea how this works out?

 

[Astronuc]

(Hint: the field within the whole is the superposition of the field due to the original uncut sphere, plus the field due to a sphere the size of the hole with a uniform negative charge density -omega)

The original charge I guess is q, and one superimposes a field of similar charge density (, but negative, as in -omega) on the smaller sphere of the diameter of the hole.

For a sphere the electric field outside the sphere is the same as a point charge of the same magnitude.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesph.html#c2

 

[benndamann33]

Yeah, the trick to the problem was actually that you can't treat the cut out as a sphere, you treat it as a disk and inherently an infinite plane. The hint about radius cutout being very small was that you treat it as one dimensional. The radius cancels out if you treated them both as a sphere and without a specific radius for each I don't believe the problem would be solvable if you went about it as that superposition. But if you treat it as an infinite plane then it was solvable. Thanks for your help