Problem No 2

Consider a brick-shaped ferromagnetic of relative magnetic permeability µ >> 1, which has dimensions 2a × 2a × a and a narrow slit of width d and depth a sawed into it as shown in Figure. You may assume that  µd >> a >> d. A circular loop of diameter a and inductance L, made of a superconducting material, is put into that slit; the loop carries electric current I. What is the mechanical work A needed to be done in order to pull the loop out of the slit and move it to a large distance from the ferromagnetic?

Remarks: (a) the inductance of the loop equals to L when it is far away from the ferromagnetic. (b) The current in the loop equals to I when the loop is inside the slit. (c) You may assume that the hysteresis of the ferromagnetic is negligible, and µ is constant (independent of B).