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

Question

A circular coil with a cross-sectional area of

4 \mathrm{~cm}^2

has 10 turns. It is placed at the center of a long solenoid that has 15 turns

/ \mathrm{cm}

and a crosssectional area of

10 \mathrm{~cm}^2

, as shown in the figure. The axis of the coil conicides with the axis of the solenoid. What is their mutual inductance? 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

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

Quantrex Academy · Accepted Answer

Correct answer: A. 7.54 μ H

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 =B_2 A_1= (μ_ 0 n_2 I_2) A_1 where n_2=N_2 / l=1500 turns / m . The mutual inductance is aligned & M= N_1 _ 12 I_2 =μ_0 n_2 N_1 A_1 & =(4 π ×10^ -7 ~T · m/ A)(1500 ~m^ -1 )(10)(4 ×10^ -4 ~m^2) & =7.54 ×10^ -6 H aligned

A circular coil with a cross-sectional area of 4 ~cm^2 has 10...

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