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_(0)I)/(2R)*`
Magnatic flux linked with smaller coil `= (mu_(0)I)/(2R) xx pir^(2)`
`M = (phi)/(I) = (mu_(0)pi r^(2))/(2R)`
`:. M prop (r^(2))/(R )`