An infinitely long, thin conducting circular cylinder of radius b is split in four quarter...

An infinitely long, thin conducting circular cylinder of radius b is split in four quarter-cylinders, as shown in Fig. The quarter-cylinders in the second and fourth quadrants are grounded, and those in the first and third quadrants are kept at potentials V0 and -V0, respectively. Determine the potential distribution both inside and outside the cylinder.

Figure: Cross section of long circular cylinder split in four quarters