A toroidal solenoid has a mean radius r and a cross-sectional area A and is wound unifonnly with N, tums. A second toroidal solenoid with N2 tums is wound unifonnly around the first. The two coils are wound in the same direction.
(a) Derive an expression for the inductance L1 when ouly the first coil is used and an expression for L2 when ouly the second coil is nsed.
(b) Show that M2 =L1 L2.