Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area `A=10 cm^(2)` and length =20cm. If one of the solenoid has 300 turns and the other 400 turns, their mutual indcutance is

Options

A. `4.78 pi xx 10^(-5)H`
B. `2.4 pixx 10^(-4) H`
C. `2.4 pixx 10^(-5) H`
D. `4.8pi xx 10^(-4) H`

Answer

B

Explanation

`M = mu_(0) n_(1) n_(2) pi r_(1)^(2) l`
From `phi_(2) = pi_(1)^(2)(mu_(0) n i)n_(21)`
`A = pi r_(1)^(2) = 10 cm^(2), l = 20 cm, N_(1) = 300`,
`N_(2) = 400`
`M = (mu_(0) N_(1)N_(2)A)/(l)`
`(4pi xx 10^(-7) xx 300 xx 400 xx 10 xx 10^(-4))/(0.20)`
`= 2.4 pi xx 10^(-4) H`