The magnetic field at the origin due to the current flowing in the wire is
Diffcult
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$B_{O D}=0$
$B_{O B}=0$
$\mathrm{B}_{\mathrm{AB}}=\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{a} \sqrt{2}}\left[\cos 45^{\circ}(-\hat{\mathrm{i}})+\cos 45^{\circ}\, \hat{\mathrm{k}}\right]$
$=\frac{\mu_{0} I}{8 \pi a}(-\hat{i}+\hat{k})$
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