Two identical long conducting wires AOB and COD are placed at right angle to each other, such that one is above the other and O is their common point. The wires carry I 1 and I 2 currents, respectively. Point P is lying at distance d from O along a direction perpendicular to the plane containing the wires. The magnetic field at the point P will be
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As from question,

The point P is lying at a distance d along the Z-axis.

As magnetic field B 1 is given by

and magnetic field B 2 is given by

B 1 and B 2 are perpendicular to each other
So,
is given by


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