Two identical small bar magnets each of dipole moment $3 \sqrt{5} \mathrm{~J} / \mathrm{T}$ are placed at a center to center separation of 10 cm , with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point $P$ midway between the magnets is $\alpha \times 10^{-3} T$. The value of $\alpha$ is $\_\_\_\_$ . $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}\right)$ [JEE MAIN_040426_S2][EMF_K] [M0derate]