An infinitely long, solid cylinder of charge with constant positive charge density, po, is concentric with an infinite cylindrical shell of charge per unit length, -A, where is a positive quantity. Both cylinders have their axes aligned with the z axis. The radius of the solid cylinder is a and that of the shell is b. Assume b > a. Po a. Find the electric potential as a function of radial distance, r, from the z axis for r< b taking p(r=0) = 0. b. Under what condition on the parameters of the problem will the electric field outside the cylindrical shell be zero? For this situation, evaluate the potential energy per unit length (along the cylinders) associated with the arrangement of charges.

An infinitely long, solid cylinder of charge with constant positive charge density, po, is concentric with an infinite cylindrical shell of charge per unit length, -A, where is a positive quantity. Both cylinders have their axes aligned with the z axis. The radius of the solid cylinder is a and that of the shell is b. Assume b > a. Po a. Find the electric potential as a function of radial distance, r, from the z axis for r< b taking p(r=0) = 0. b. Under what condition on the parameters of the problem will the electric field outside the cylindrical shell be zero? For this situation, evaluate the potential energy per unit length (along the cylinders) associated with the arrangement of charges.