A circular coil with a cross-sectional area of 4 ~cm ^2 has 10 turns. It is placed at the center of a long solenoid that has 15 turns / cm and a crosssectional area of 10 ~cm ^2 , as shown in the figure. The axis of the coil conicides with the axis of the solenoid. What is their mutual inductance?

Step-by-step solution

Let us refer to the coil as circuit 1 and the solenoid as circuit 2 . The field in the central region of the solenoid is uniform, so the flux through the coil is ₁₂=B₂ A₁= ( ₀ n₂ I₂ ) A₁ where n₂=N₂ / l=1500 turns / m . The mutual inductance is aligned & M= N₁ ₁₂ I₂ = ₀ n₂ N₁ A₁ & = (4 10⁻⁷ ~T m / A ) (1500 ~m ⁻¹ )(10) (4 10⁻⁴ ~m ^2 ) & =7.54 10⁻⁶ H aligned