3. An infinite cylinder of radius R is made of a linear dielectric material with the electric suscep- tibility Xe: The cylinder is extended along the z-axis and the center axis is located at (x, y, z) (0,0, 2). This cylinder is placed in an otherwise uniform electric field Eo to use the solution of the Laplace equation to answer the following questions. Eo. You are supposed (a) Find the general solution for the potential Vin inside the cylinder, and Vout Ooutside the cylinder. Make sure that the general solution has no singularity. (b) What are the appropriate boundary conditions ? (c) Find Vin and Vout that satisfy the boundary conditions. Find the electric field inside the cylinder.