3) A permanent magnet is levitated above the HTS with a field cooling height h. The permanent magnet is represented by a magnetic dipole moment m, which is aligned along the horizontal direction ( mp = ma, and m is the magnitude of the moment). a) Obtain the vertical force between the superconductor and the permanent magnet as a function of vertical distance (2) between the PM and the surface of the HTS, field cooling height (h), horizontal displacement (r) and magnetic moment of the PM (m). b) Obtain the lateral (guidance) force between the superconductor and the permanent magnet as a function of vertical distance (2) between the PM and the surface of the HTS, field cooling height (h), horizontal displacement (r) and magnetic moment of the PM (m). c) Calculate the ratio of the forces: the value of the vertical force at z = zo for the case of zero field cooling with horizontal displacement of r= zo and value of the vertical force for the case of field cooling height h=zo with no horizontal displacement r=20.25P 3) A permanent magnet is levitated above the HTS with a field cooling height h. The permanent magnet is represented by a magnetic dipole moment m, which is aligned along the horizontal direction ( mp = ma, and m is the magnitude of the moment). a) Obtain the vertical force between the superconductor and the permanent magnet as a function of vertical distance (2) between the PM and the surface of the HTS, field cooling height (h), horizontal displacement (r) and magnetic moment of the PM (m). b) Obtain the lateral (guidance) force between the superconductor and the permanent magnet as a function of vertical distance (2) between the PM and the surface of the HTS, field cooling height (h), horizontal displacement (r) and magnetic moment of the PM (m). c) Calculate the ratio of the forces: the value of the vertical force at z = zo for the case of zero field cooling with horizontal displacement of r= zo and value of the vertical force for the case of field cooling height h=zo with no horizontal displacement r=20.25P