1. The problem statement, all variables and given/known data A long insulating cylinder of radius R1 has a cylindrical hole parallel to the axis of the cylinder. The radius of the hole is R2, and the distance from the centre of the cylinder to the centre of the hole is a. There is a uniform fixed charge per unit volume ρ throughout the cylinder, except in the hole where there is no charge. Using a cylindrical coordinate system with the z axis along the centre of the cylinder, evaluate the components of the electric field inside the cylinder and inside the hole (you may neglect edge effects at the ends of the cylinder). 2. Relevant equations Gauss' law 3. The attempt at a solution I know I need to use superposition. I would like to: Calculate the electric field of the cylinder of radius R1 alone with no hole. I did so to get E1=0.5ρr for r≤R1. Calculate the electric field of the cylinder of radius R2 alone with charge in it (not easy!) Subtract the fields from the second calculation from the first. The major problem is that my cylindrical coordinate system is centred on the large cylinder. How can I compute the electric field in and around the second cylinder with such a coordinate system? I want a cylindrical Gaussian surface around the cylinder of radius R2. I just can't see how to do it :/ Thanks in advance.