Dielectric layer radiation

This should be a very simple project to an electrical engineer. The problem is described per the attachment. Project tasks: 1) Verify the differential equations 2) The radiation interaction between the two cylinders. Describe the differential equation of cylinder 1 in cylinder 2 coordinate system. 3) If the middle layer is piezoelectric. How to describe the electrical interaction i.e. use of task 2 4) If an electrode is connected to the middle layer i.e. the electric potential is symmetric (the same value)