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Physics Question on Moving charges and magnetism

Which one of the following options represents the magnetic field B⃗\vec{B} at OO due to the current flowing in the given wire segments lying on the xyx y plane?
wire segments lying on

A

B⃗=−μ0IL(32+142π)k^\vec{B}=\frac{-\mu_0 I}{L}\left(\frac{3}{2}+\frac{1}{4 \sqrt{2} \pi}\right) \hat{k}

B

B⃗=−μ0IL(32+122π)k^\vec{B}=-\frac{\mu_0 I}{L}\left(\frac{3}{2}+\frac{1}{2 \sqrt{2} \pi}\right) \hat{k}

C

B⃗=−μ0IL(1+142π)k^\vec{B}=\frac{-\mu_0 I}{L}\left(1+\frac{1}{4 \sqrt{2} \pi}\right) \hat{k}

D

B⃗=−μ0IL(1+14π)k^\vec{B}=\frac{-\mu_0 I}{L}\left(1+\frac{1}{4 \pi}\right) \hat{k}

Answer

B⃗=−μ0IL(1+142π)k^\vec{B}=\frac{-\mu_0 I}{L}\left(1+\frac{1}{4 \sqrt{2} \pi}\right) \hat{k}

Explanation

Solution

Current flowing in the given wire segment is B⃗=−μ0IL(1+142π)k^\vec{B}=\frac{-\mu_0 I}{L}\left(1+\frac{1}{4 \sqrt{2} \pi}\right) \hat{k}