A solenoid of lenght 30 cm with 10 turns per centimetre and area of cross-section `40cm^(2)` completely surrounds another co-axial solenoid of same length, area of cross-section `20cm^(2)` with 40 turns per centimetre. The mutual inductance of the system is

Options

A. 10 H
B. 8 H
C. 3 mH
D. 30 mH

Answer

C

Explanation

Mutual inductance of the system,
`M=mu_(0)n_(1)n_(2)A_(2)l`
where `A_(2)` is the area of inner solenoid.
`n_(1)=10 cm^(-1)=1000 m^(-1)`
`n_(2)=40 cm^(-1)=4000 m^(-1)`
`l=30 cm=30xx10^(-2)m`
`A_(2)=20cm^(2)=20xx10^(-4)m^(2)`
`:.M=4pixx10^(-7)xx1000xx4000xx20xx10^(-4)xx30xx10^(-2)`
`=301.44xx10^(-5)H=3mH`