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
` vecB_1 = (mu_0 i_1 R^2)/(2(R^2 + R^2)^(3//2) ) ` to left magnetic induction at 0 due to 2nd loop
` vecB_2 = (mu_0 i_2 R^2)/(2 (R^2 + R^2)^(3//2) ) ` to right ` vecB_1 + vecB_2 = 0`
` rArr (i_2)/((2R^2)^(3//2) ) - (i_1)/((R^2 + x^2)^(3//2) ) " and " i_2 = 8i_1 rArr x = sqrt7 R`