Question

Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current $I_1$ and COD carries a current $I_2$. The magnetic field on a point lying at a distance d from O, in a direction perpendicular to the plane of wires AOB and COD will be given by

Answer 1

Magnetic field due to AB and CD are $\frac{{\mu }_0}{2\pi d}$ and $\frac{{\mu }_0{I}_2}{2\pi d}$ respectively and are in mutually perpendicular direction.
$B_{net}=\frac{{\mu }_0}{2\pi d}\sqrt{I_1^2+I_2^2}$