Two wires are wrapped over a wooden cylinder to form two coaxial loops carrying currents `i_(1)` and `i_(2)`. If `i_(2) = 8i_(1)` then find tlte value of x for B = 0 at the origin O

Explanation

Magnetic induction at .O. due to 1st loop
`vecB_(1)=(mu_(0)i_(1)R^(2))/(2(R^(2)+R^(2))^(3//2))` to left Magnetic induction at .O. due to 2nd loop
`vecB_(2)=(mu_(0)i_(2)R^(2))/(2(R^(2)+x^(2))^(3//2))` to right `vecB_(1)+vecB_(2)=0`
`rArr(i_(1))/((2R^(2))^(3//2))-(i_(1))/((R^(2)+x^(2))^(3//2))` and `i_(2)=8i_(1)rArrx=sqrt7R`