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

The self inductance of the solenoid is

(A) πn²l[μ₁b²+μ₂a²]

(B) πn²l[μ₁+μ₂]a²

(C) πn²l [μ₁b² +μ₂(a²-b²)]

(D)πn² [μ₁b²+(μ₁+μ₂)a²]

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