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

Options

A. `7.54 muH `
B. `8.54 mu H `
C. `9.54 mu H`
D. ` 10.54 mu H `

Answer

A

Explanation

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 `Phi_12=B_(2)A_(1)=(mu_(0)n_(2)l_(2))A_(1)`
Where `n_2=N_(2)//l=1500` turns/m. The natural inductance is `M=(N_(1)Phi_(12))/(l_(2))=mu_(0)n_(2)N_(1)A_(1)`
`=(4pixx10^(-7)T.m//a)(1500m^(-1))(10)(4xx10^(-4)m^(2))`
`=7.54xx10^(-6)H`