A thin superconducting(zero resistance) ring a held above a vertical long solenoid, as shown in the figure. The axis of symmetry of the ring is same to that of the solenoid. The cylindrically symmetric magnetic field around the ring can be described approximately in terms of the vertical and radial component of the magnetic field vector as B_(z) = B_(0)(1-alpha z) and B_(r) = B_(0) beta r, where B_(0),alpha and beta are positive constants, and z & r are vertical and radial position coordinates, respectively, Initially plane of the ring is horizontal has no current flowing in it. When relreased, it starts to move downwards with its axis axisstill vertical. Initial coordinates of the centre of the ring 'O' is z = 0 and r =0. In the given diagram point O is on the axis and slightly above the solenoid having vertical and radial position coordinates as (0,0) Ring has mass m, radius m, radius r_(0) and self inductance L. Assume the acceleration due to gravity as g. Find the vertical coordinates z for equilibrium position of the ring.