An infinitely long conducting cylinder of radius a is centered at the origin and oriented along the z axis. It is cut by the x-z plane into two hemicylinders, and the hemicylinders are insulated from each other. The hemicylinder at y>0 is held at a positive potential V while the hemicylinder at y<0 is held at a negative potential -V. It is surrounded by another second cylinder at radius b, coaxial with the first cylinder, which is grounded. Find an expression for the potential at all points between the two cylinders.