A long solenoid of length `L`, cross section `A` having `N_(1)` turns has about its center a small coil of `N_(2)` turns as shows in Fig The mutual inductance of two circuits is

Options

A. `mu_(0)u_(r)(N_(1)N_(2))/(l)`
B. `(mu_(0)u_(r)N_(1)N_(2))/(Al)`
C. `mu_(0)u_(r)N_(1)N_(2)Al`
D. `(mu_(0)u_(r)N_(1)N_(2)A)/(l)`

Answer

D

Explanation

Coefficient of mutual inductance,
`M=(phi)/(l_(p))=(mu_(0)u_(r)N_(1)N_(2)N_(2)Al_(p))/(II_(p))=(mu_(0)u_(r)N_(1)N_(2)A)/(l)`