Meissner effect in sphere considers a sphere of a type 1 super conductor with critical field H

Question:

Meissner effect in sphere considers a sphere of a type 1 super conductor with critical field H_c.

(a) Show that in the Meissner regime the effective magnetization M within the sphere is given by –8πM/3 = B_a, the uniform applied magnetic field.

(b) Show that the magnetic field at the surface of the sphere in the equatorial plane is 3B_n/2. (It follows that the applied field at which the Meissner affect starts to break down is 2H_c/3.) Reminder: The demagnetization field of a uniformly magnetized sphere is – 4πM/3.