A small coil of radius `r` is placed at the centre of a large coil of radius `R`, where `R gtgt r`. The two coils are coplanar. The mutual inductance between the coils is proportional to

Options

A. `(mu_(0)pir^(2))/(2R)`
B. `(mu_(0)pir^(2))/(R)`
C. `(2mu_(0)pir^(2))/(R)`
D. `(3mu_(0)pir^(2))/(2R)`

Answer

A

Explanation

Magnetic field at the centre of large coil can be written as follows when I current flows through it.
`B= mu_(0)(I)/(2R)`
Other coil is small and hence we can assume uniform magnetic field over it. Magnetic flux linked with the small coil can be written as follows:
`phi= Bpir^(2)= (mu_(0)pir^(2)I)/(2R)`
`phi = MI`
`M= (mu_(0)pir^(2))/(2R)`