Eletric field within a cavity of a cylinder.

[PenKnight]

Homework Statement

Considering a cylinder of radius, R, and length D with uniform charge density p containing a spherical cavity of radius R/2. Find the field in the cavity.

The cavity sits on one side of the cylinder so that it's diameter spans from the concave face of the cylinder to the center.I'm not sure at what length the cavity is. Probably at D/2. I think that D > R as well.

The Attempt at a Solution

I'm not sure where to start. The only thing that is symmetrical about this problem is that you can cut the shape in half and have two mirror pieces.

 

[member 553083]

I'm thinking that you could use Gauss's Law somehow, but I'm not sure how to apply it. I'm guessing that the field should be zero, as the charge is distributed uniformly and the charge inside the cavity is equal to the charge outside the cavity.