Hollow Cavity within a charged sphere

[Lancen]

Suppose I had a uniformly charged sphere of some density, inside this sphere at some position there is a cavity of some radius. If I wanted to then find the Electric field somewhere, like say the surface of the sphere, how would I approach the problem?

Heres what I did. I pretended the cavity didn't exist and using Gauss' Law found the electric field at the surface of the sphere to be p*R/3*e, where p is charge density, R is the radius of the sphere and e is the electrical permittivity. Then I found the electric field for the cavity which has a radius of R/2 and is located in such a way that the distance from its center to the surface of the charged sphere is 3/2*R. and that was 4.5*(p)*R/e. Thats where I am stuck. As I was doing this I thought I could treat this like those moment of inertia problems where you have a piece of a wheel or something missing and you just treat that piece as negative mass. But then when I went to do this, I realized all I would be doing if I subtracted the field off off the cavity would be adding a negative field. Also, if it is just a cavity is there even a field inside it?

 

[member 553083]

Yes, there will be an electric field inside the cavity. The electric field inside a cavity in a uniformly charged sphere is just the same as the electric field outside the sphere, and can be calculated using Gauss' Law.