Two conducting circular loops of radii `R_1` and `R_2` are placed in the same plane with their centres coinciding. If `R_1` >> `R_2` the mutual inductance M between them will be directly proportional to

Options

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

Answer

C

Explanation

Magnetic field at the centre of primary coil-
`B = (u_(0)i_(1))/(2R_(1))`
Considering it to be uniform, magnetic flux passing through secondary coil is-
`phi_(2) = AB = (mu_(0)i_(1))/(2R_(1)) (piR_(2)^(2))`
Now, `M = phi_(2)/i_(1) = (mu_(0)piR_(2)^(2))/(2R_(1))`
`therefore M prop R_(2)^(2)/R_(1)`