A cylindrical iron core of relative permeability ur is of radius a and length l, where l >> a. N1 turns of wiere are closely wound around the core over its entire length, and current I1 is fed to the coil. In addition, N2 turns of wire are wound as a second layer on top of the first coil, again over the entire length of the core. Current I2 is fed to this second coil. Both turn layers have negligible thickness.
a) Determine the self inductance of coil 1, L11
b) Determine the self inductance of coil 2 L22
c) Determine the mutual inductance between the two coils, L12 or L21