Finding Electric Field in Spherical Hole

[du_uk]

Homework Statement

A spherical hole is located inside a uniformly charged sphere of charge density p. The centre of the hole is at a distance a from the centre of the sphere, and the radii of the sphere and the hole are given by R and R' respectively. Determine the electric field strength E inside the hole.

Homework Equations

The Attempt at a Solution

I think I need to use Gauss's law the find the electric field around this red surface:
http://img20.imageshack.us/img20/6870/electroqy.jpg
and since there is symmetry, integrate around 0 to 2(pi) wrt the extra (third dimensional) coordinate.
Then minus the electric field for a sphere outside the charge.

Am I going about this the right way?

Thanks

 

[gabbagabbahey]

Hi du_uk, welcome to PF!

I think I need to use Gauss's law the find the electric field around this red surface:
http://img20.imageshack.us/img20/6870/electroqy.jpg
and since there is symmetry, integrate around 0 to 2(pi) wrt the extra (third dimensional) coordinate.
Then minus the electric field for a sphere outside the charge.

Am I going about this the right way?

I'm not sure exactly what you mean here, but no, you are not going in the right direction. What exactly is the symmetry you are referring to here?

Instead, take advantage of the superposition principle...what happens if you place an object of charge density $-\rho$ inside a larger object of charge density $+\rho$?

 

[Phrak]

More to the point, place a spherical charge density $-\rho$ inside a larger spherical charge density $+\rho$. What are the forces inside the smaller sphere?