Two wires wrapped over a conical frame from the coils `1` and `2`. If they produce no net magnetic field at the apex `P`, the value of

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)=i^(2)implies(r^(2)+x^(2))^(3//2)=l^(3)`
where`'l'` is slant length `B=(mu_(0)i)/(2r)((r)/(l))^(3)`. But `(r)/(l)=sin phi`
where `phi` is apex angle, same for both the loops
`vec(B)_(1)+vec(B)_(2)=(` given)`impliesB_(1)=B_(22)implies(i_(1))/(i_(2))=(r_(1))/(r_(2))`