O is the centre of two coplanar concentric circular conductors, A and B, of radii r and R respectively as shown in the figure. Here, `r lt lt lt R`. The mutual inductance of the system of the conductors can be given by

Options

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

Answer

A

Explanation

Mutual inductance for two concentric complanar circular coils,
`M=(pimu_(0)N_(1)N_(2)r^(2))/(2R)`
Here, `N_(1)=N_(2)=1`
`therefore M=(pimu_(0)r^(2))/(2R)`