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. `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 a current `I_1` flows through the outer circular coil of radius `R_1`.
The magnetic field at the centre of the coil is B =`(mu_0 I_1)/(2R_1)`
As the inner coil of radius `R_2` placed co-axially has small radius `(R_2 lt R_1)` , therefore `B_1` may be taken constant over its crosssectional area. Hence, flux associated with the inner coil is
`phi_2 = B_1 pi R_2^2 = (mu_0 I_1)/(2R_1) pi R_2^2`
As `M = (phi_2)/(I_1) = (mu_0 pi R_2^2)/(2R_1) therefore M prop (R_2^2)/(R_1)`