Question

A (long thin) solenoid core has an insulated primary coil, (of n₁ turns per unit length) and an insulated secondary coil, (of n₂ turns per unit length) wound on top of the primary coil. The cross sectional area of the solenoid, equals A. 

If L₁ and L₂ are the self inductances of the two coils and M is their coefficient of mutual inductance, we would have (in the ideal case).

(1) M = \(\frac{(L^3_1)}{(L^2_2)}\)

(2) M = \(\sqrt{L_1L_2}\)

(3) M = \((\frac{L^2_1}{L^2_2})\)

(4) M = \((\frac{L^2_2}{L_1})\)

Answer 1

(2) M = \(\sqrt{L_1L_2}\)

The self inductance, L₁ and L₂ , of the two solenoid coils, are given by

when μ is the magnetic permeability of the core material and l is the length of the solenoid. Also M, the coefficient of mutual industance, is going by

M = μn₁ n₂ Al

We, therefore, have L₁ L₂ = M² or M = \(\sqrt{L_1L_2}\)