The conducting circular loops of radii `R_(1) and R_(2)` are placed in the same plane with their centres coinciding. If `R_(1) gt gt R_(2)`, the mutual inductance M between them will be directly proportional to

Options

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

Answer

D

Explanation

Let acurrent `I_(1)` flows through the outer circular col of radius `R_(1)`.
The magnetic field at the centre of the coil is
`B_(1)=(mu_(0)I_(1))/(2R_(1))`
As the inner coil of radius `R_(1)`placed co-axiallu has small radius `(R_(2)-R_(1))`, therefore, `B_(1)` may be takne constant over its corss-sectional area.
Hence, flux associated with the inne coil is
`phie_(2)B_(1)piR_(2)^(2)=(mu_(0)I_(1))/(2R_(1))piR_(2)^(2)`
As `M=(phi_(2))/(I_(1))=(mu_(0)R_(2)^(2))/(2R_(1))`
`:. M prop((R_(2)^(2)))/(R_(1))`