Equal currents are flowing in three infinitely long wires along positive $x, y$ and $z$ direction. The magnetic field at a point $(0, 0, -a)$ would be ( $i =$ current in each wire)
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at $(0,0,-a)$ magnetic field due to wire along $ \mathrm{x}$ $-$ axis is
$B_{1}=\frac{\mu_{0} I}{2 \pi Q} \hat{J}$
due to wire along $\mathrm{y}$ $-$ axis
$\mathrm{B}_{2}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{a}}(-\hat{\mathrm{i}})$
due to wire along $\mathrm{Z}$ $-$ axis
${\mathrm{B}_{3}=0} $
${\mathrm{B}_{\mathrm{net}}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{a}}(\hat{j}-\hat{\mathrm{i}})}$
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