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

224408-q

  • [IIT 2022]
  • A

    $\vec{B}=\frac{-\mu_0 I}{L}\left(\frac{3}{2}+\frac{1}{4 \sqrt{2} \pi}\right) \hat{k}$

  • B

    $\vec{B}=-\frac{\mu_0 I}{L}\left(\frac{3}{2}+\frac{1}{2 \sqrt{2} \pi}\right) \hat{k}$

  • C

    $\vec{B}=\frac{-\mu_0 I}{L}\left(1+\frac{1}{4 \sqrt{2} \pi}\right) \hat{k}$

  • D

    $\vec{B}=\frac{-\mu_0 I}{L}\left(1+\frac{1}{4 \pi}\right) \hat{k}$

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