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 \( xy \) plane?
\( \vec{B} = \dfrac{-\mu_{0} I}{L} \left( \dfrac{3}{2} + \dfrac{1}{4\sqrt{2}\pi} \right) \hat{k} \)
\( \vec{B} = -\dfrac{\mu_{0} I}{L} \left( \dfrac{3}{2} + \dfrac{1}{2\sqrt{2}\pi} \right) \hat{k} \)
\( \vec{B} = \dfrac{-\mu_{0} I}{L} \left( 1 + \dfrac{1}{4\sqrt{2}\pi} \right) \hat{k} \)
\( \vec{B} = -\dfrac{\mu_{0} I}{L} \left( 1 + \dfrac{1}{4\pi} \right) \hat{k} \)
