Magnetic Effects of Current and Magnetism: JEE Main 2026 Physics question

Two identical small bar magnets each of dipole moment $3\sqrt5$ J/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 $\alpha\times10^{-3}$ T. The value of $\alpha$ is ______. ($\mu_0=4\pi\times10^{-7}$ Tm/A)