Two wires wrapped over a conical form the loops 1 and 2. If they produce no net magnetic field at the apex P, find the value of `(i_(1))/(i_(2))`

Explanation

Magnetic induction due to a loop at apex,
`B=(mu_(0)ir^(2))/(2(r^(2)+x^(2))^(3//2))`
But `r^(2)+x^(2)=l^(2)rArr(r^(2)+x^(2))^(3//2)=l^(3)` where .l. is slant length `B=(mu_(0)i)/(2r)(r/l)^(3)`
But `r/l=sinphi` where `phi` is apex angle, same for both the loops `vecB_(1)+vecB_(2)=0` (given) `rArrB_(1)=B_(2)rArr(i_(1))/(i_(2))=(r_(1))/(r_(2))`