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 coincide with the axis of the solenoid. What is their mutual inductance?

Options

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

Answer

A

Explanation

Let us refer to the coil as circuit 1 and the soleniod circuite 2. The field in the central region of the solenoid is uniform, so the flux through the coil is
`phi_(12)=B_(A)A_(1)=(mu_(0)n_(2)I_(2))A_(1)`
where `n_(2)=N_(2)//l=1500` turn/m
The mutual inductance si
`M=(N_(2)phi_(12))/(I_(2))=mu_(0)n_(2)N_(1)A_(1)`
`=(4pixx10^(-7)Tm A^(-1))(1500m^(-1))(10)(4xx10^(-4)m^(2))`
`7.54xx10^(-6)H=7.54 muH`