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)A(N_(1))//N_(2))/(L)`
B. `(mu_(0)AN_(1)N_(2))/(L)`
C. `mu_(0)AN_(1)N_(2)L`
D. `(mu_(0)AN_(1)//N_(1)^(2))/(L)`

Answer

B

Explanation

`varphi_(0)=N_(2)B_(1)A`
or `varphi_(2)=N_(2)(mu_(0)N_(1)N_(2)A)/(L)`
or`=varphi_(2)=(mu_(0)N_(1)N_(2)A)/(L)I-2`
comparing with `varphi_(2)=MI_(1),we g et(mu_(0)N_(1)N_(2)A)/(L)`