Problem: A long cylinder of diameter 2a has a charge per unit length, lambda, that is uniformly distributed down a very long wire. The cross section of the cylinder is not uniform, with a small hole drilled into it, which has a center at r = R and a diameter of 2b. Find an expression for the electric field outside this surface at a distance r = 3a/2.

Question

Problem:  A long cylinder of diameter 2a has a charge per unit length, lambda, that is uniformly distributed down a very long wire. The cross section of the cylinder is not uniform, with a small hole drilled into it, which has a center at r = R and a diameter of 2b. Find an expression for the electric field outside this surface at a distance r = 3a/2.

Approach:   So do I just find the field due to the large cylinder and then subtract what the field would be due to a cylinder the size of the hole.  How do I account for the hole being offset?