Two insulating infinitely long wires are lying mutually perpendicular to each other as shown in fig.

The magnetic field at point P (a,b), will be

The magnetic fields at P due to the wires are
${\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{2{\mathrm{i}}_1}{\mathrm{a}}$ (in inward direction)
${\mathrm{B}}_2=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\cdot \frac{2{\mathrm{i}}_2}{\mathrm{b}}$ (in outward direction)
Therefore, net magnetic field at p (a, b) is
$\mathrm{B}={\mathrm{B}}_2-{\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\left[\frac{2{\mathrm{i}}_2}{\mathrm{b}}-\frac{2{\mathrm{i}}_1}{\mathrm{a}}\right]$