A toroidal core has a rectangular cross section defined by the surfaces a = 2 cm, b = 3 cm, z = 4 cm, and z = 4.5 cm. The core material has a relative permeability of 80. The core is wound with two coils having N1 = 1000 and N2 = 2500 turns of wire.
a) Find the self inductances of the two coils.
b) Find the mutual inductance between the two coils.