The magnetic field at the origin due to the current flowing in the wire is -
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$B _{ OD }=0$
$B _{ OB }=0$
$B _{ AB }=\frac{\mu_0}{4 \pi a \sqrt{2}}\left[\cos 45^{\circ}(-\hat{1})+\cos 45^{\circ} k \right]$
$=\frac{\mu_0}{8 \pi a }(-\hat{i}+\hat{ k })$
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