Two concentric coplanar circular loops of radii `r_(1)` and `r_(2)` carry currents of respectively `i_(1)` and `i_(2)` in opposite direction (one clockwise and the other anticlockwise). The magnetic induction at the centre of the loops is half that due to `i_(1)` alone at the centre. if `r_(2)=2r_(1)`. the value of `i_(2)//i_(1)` is

Options

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

Answer

D

Explanation

`B_(1)=(mu_(0)i_(1))/(2r_(2)), B_(2)=(mu_(0)i_(2))/(4r_(1))`
`B_(0)=B_(1)-B_(2)=(mu_(0))/(4r_(1))(2i_(1)-i_(2))`
`B_(0)=1/2B_(1)`
`(mu_(0))/(4r_(1))(2i_(1)-i_(2))=1/2. (mu_(0)i_(1))/(2r_(1))`
`2i_(1)-i_(2)=i_(1)`
`(i_(2))/(i_(1))=1`