A familiar demonstration of superconductivity (Problem. 7.42) is the levitation of a magnet over a piece of

Question:

A familiar demonstration of superconductivity (Problem. 7.42) is the levitation of a magnet over a piece of superconducting matedhal. This phenomenon can be analyzed using the method of images. 19 Treat the magnet as a perfect dipole m, a height z above the origin (and constrained to point in the z direction), and pretend that the superconductor occupies the entire half-space below the xy plane. Because of the Meissner effect, B = 0 for z 0.

(a) Which way should the image dipole point (+ z or ?? z)?

(b) Find the force on the magnet due to the induced currents in the superconductor (which is to say, the force due to the image dipole). Set it equal to Mg (where M is the mass of the magnet) to determine the height h at which the magnet will "float."

(c) The induced current on the surface of the superconductor (the xy plane) can be determined from the boundary condition on the tangential component of B (Eq. 5.74): B = ?0 (K x z,). Using the field you get from the image configuration, show that where r is the distance from the origin.