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. `r//R`
B. `r^2//R`
C. `r^2//R^2`
D. `r//R^2`

Answer

B

Explanation

Magnetic field at the centre of a large coil `E prop (mu_0I)/(2R)`
Magnetic flux linked with smaller ocil `=(mu_0I)/(2R)xxpir^2`
`M=phi/I=(mu_0pir^2)/(2R), therefore M prop (r^2)/R`