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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

μ0I2πdcosϕ1+cosϕ2

b

μ04π2Idtanθ1+tanθ2

c

μ04πIdsinϕ1+sinϕ2

d

μ04πIdcosθ1+sinθ2

answer is A.

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Detailed Solution

Using B=μ0I4πdsinθ1+sinθ2  But θ1+ϕ1=90° or θ1=90°-ϕ,  sinθ1=sin90°-ϕ1=cosϕ1  Similarly,   sinθ2=cosϕ2Bnet =μ0I2πdcosϕ1+cosϕ2
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