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

A circular coil with a cross-sectional area of `4cm^(2)` has 10 turns.

1.	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? A. `7.54muH`B. `8.54muH`C. `9.54muH`D. `10.54muH`
Answer» Correct Answer - A 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`

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