The magnetic field at O due to current in the infinite wire forming a loop as shown in figure is

B=μ0I4πd   sinθ1  +  sinθ2But θ1=900-φ1 and θ2=900 -φ2sin  θ1 =  sin 900  −  ϕ1  =  cos ϕ1Similarly sin θ2 =  cos ϕ2 .Magnetic field on the axis of a current carrying conductor is zero B=μ0I4πd cos ϕ1  +  cos ϕ2