Two wires are wrapped over wooden cylinder to form two co-axial loops carrying currents `i_(1)` and `i_(2)`. If `i_(2)=8i_(1)` the value of `x` for `B=0` at the origin `O` is:

Explanation

Magnetic induction at `'0'` due to `1st` loop
`vec(B)_(1)=(mu_(0)i_(1)R^(2))/(2(R^(2)+R^(2))^(3//2))` to left Magnetic induction at `'0'` due to `2nd` loop.
`vec(B)_(2)=(mu_(0)i_(2)R^(2))/(2(R^(2)+R^(2))^(3//2))` to riight `vec(B)_(1)+vec(B)_(2)=0`
`implies(i_(1))/((2R^(2))^(3//2))-(i_(1))/((R^(2)+x^(2))^(3//2))` and `i_(2)=8i_(22)impliesx=sqrt(7)R`