`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

`r_(1):r_(2)=1:2` and `B_(1):B_(2)=1:3` we know that
`B=(mu_(0))/(4pi).(2pini)/r implies (i_(1))/(i_(2))=(B_(1)r_(1))/(B_(2)r_(2))=(1xx1)/(3xx2)=1/6`