Electric Field Uniformity in a Sphere with Cavity

[phantom113]

Homework Statement

A charge q is uniformly distributed over the volume of a solid sphere of radius R. A spherical cavity is cut out of this solid sphere and the material and its charge are discarded. Show that the electric field in the cavity will then be uniform, of magnitude kqd/r^3, where d is the distance between the centers of the spheres.

Homework Equations

principle of superposition
E=kq/r^2

The Attempt at a Solution

I'm not really sure where to start with this one. I know you can take the electric fields of the two spheres and add them together, but the cavity has no charge enclosed. Maybe I'm just reading the problem incorrectly. A push in the right direction would be terrific.

Thanks.

 

[Delphi51]

I noticed that it is easy to calculate the E field at one particular point - the center of the small sphere. The total E is the E due to the big sphere (with no hole) minus the E due to the small sphere of charge.

Perhaps you can extend the method to any point in the small sphere . . .

 

[phantom113]

OK, thanks I got the equation to work(had to assume that one part of edge of the cavity was also the edge of the sphere to get the radius of the cavity). Is the reason that it's a uniform field that the field vectors at a random point not in the middle are in opposite directions and end up canceling to the same value as the field at the middle?