UPSEE 2018 Solved Paper

A very long solenoid is made out of a wire with n turns per unit length. The radius of the cylinder is a and is negligible compared to its length l. The interior of the cylinder is filled with materials such that the linear magnetic permeability varies with the distance r from axis according to
µ(r)={

µ1=constant ; for 0<r<b

µ2=constant ;for b<r<a

}
The self-inductance of the solenoid is