Two conducting circular loops of radii `R_1 and R_2` are placed in the same plane with their centres coincidingt. Find the mutual inductane between them assuming `R_2ltltR_1`.

Options

A. `(mu_(0)piR_(2)^(2))/(2R_(1))`
B. `(mu_(0)piR_(1)^(2))/(2R_(2))`
C. `(mu_(0)piR_(2)^(2))/(R_(1))`
D. `(mu_(0)piR_(1)^(2))/(R_(1))`

Answer

A

Explanation

Magnetic field at `O` due to (1)
`B_(1)=(mu_(0)i)/(2R_(1))`
Flux through (2)
...(i) `phi=B_(1).piR_(2)^(2)=(mu_(0)i)/(2R_(1)).piR_(2)^(2)=Mi`
...(ii) `M=(mu_(0)piR_(2)^(2))/(2R_(1))`