An infinitely long solid cylinder (u = 1) of radius R oriented along the z-axis is carrying a constant current density Jo = jo(s)ez, where jo(s) = (Rs); here (r) is the Heaviside step function, which is = 0 if x < 0 and = 1 if x > 0. Calculate the magnetic vector potential A and magnetic field # inside and outside of the cylinder. To do so proceed as follows: (a) Use the Poisson equation for the vector potential to determine A outside the cylinder. (Hint: Make use of the symmetry of the vector potential A = Az(s)z.) (b) Determine A inside the cylinder. (c) Use the boundary condition Ainside = outside to determine A for all space. (d) Calculate , using also that is continuous at s = R.