Magnetic Properties of Ma question bank (Physics)

Two identical small bar magnets each of dipole moment $3\sqrt{5}$ 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 $\alpha \times 10^{-3}$ T. The value of $\alpha$ is ______.
($\mu_0=4\pi \times 10^{-7}$ Tm/A)

A solenoid has a core made of material with relative permeability $400$. The magnetic field produced in the interior of solenoid is $1.0$ T. The magnetic intensity in SI units is $\alpha \times 10^5$. The value of $\alpha$ is ______.
(Free space permeability $\mu_0=4\pi \times 10^{-7}$ SI units.)