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A circular coil with a cross-sectional a...

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

A

`7.54 muH `

B

`8.54 mu H `

C

`9.54 mu H`

D

` 10.54 mu H `

Text Solution

Verified by Experts

The correct Answer is:
A
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`
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