Question

A circular coil with a cross-sectional area of 4 cm2 has 10 turns. It is placed at the centre of a long solenoid that has 15 turns/cm and a cross-sectional area of 10 cm2, as shown in the figure. The axis of the coil coincides with the axis of the solenoid. What is their mutual inductance?

• A. 7.54$\mu \mathrm { H }$
• B. 8.54 $\mu \mathrm { H }$
• C. 9.54 $\mu \mathrm { H }$
• D. 10.54$\mu \mathrm { H }$

Answer 1

Answer: (A)

7.54$\mu \mathrm { H }$

Answer 2

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 uniforms, so the flux through the coil is

Where turns/m

The mutual inductance is

$= \left( 4 \pi \times 10 ^ { - 7 } \mathrm { TmA } ^ { - 1 } \right) \left( 1500 \mathrm {~m} ^ { - 1 } \right) ( 10 ) \left( 4 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 } \right)$

$= 7.54 \times 10 ^ { - 6 } \mathrm { H } = 7.54 \mu \mathrm { H }$