Q.

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

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a

μ0I4πd   cos ϕ1 +  cos ϕ2

b

μ04π Id  tan ϕ1 +  tan ϕ2

c

μ04π Id  sin ϕ1 +  sin ϕ2

d

μ04π Id  cos ϕ1 +  sin ϕ2

answer is A.

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Detailed Solution

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