`A` and `B` are two concentric circular conductors of centre `O` and carrying currents `i_(1)` and `i_(2)` as shown in the adjacent figure. If ratio of their radii is `1:2` and ratio of the flux densities at `O` due to `A` and `B` is `1:3`, then the value of `i_(1)//i_(2)` is

Options

A. `1//6`
B. `1//4`
C. `1//3`
D. `1//2`

Answer

A

Explanation

`B = (mu_(0) I)/(2R) implies B prop (I)/( R)`
`implies (B_(1))/(B_(2)) = (I_(1))/(I_(2)) xx (R_(2))/(I_(2)) implies (1)/(3) = (I_(1))/(I_(2)) xx 2 implies (I_(1))/(I_(2)) = (1)/(6)`