Magnetic field $\left(B_1\right)$ due to a small bar magnet at a point $P$ on the axial line is equal to magnetic field $\left(B_2\right)$ due to the same magnet at point $Q$ on equatorial line. What is the ratio of distances of point $P$ and $Q$ from centre?

Two identical short bar magnets, each having magnetic moment of $10 \mathrm{A} {\mathrm{m}}^2,$ are arranged such that their axial lines are perpendicular to each other and their centres be along the same straight line in a horizontal plane. If the distance between their centres is $0.2 \mathrm{m},$ the resultant magnetic induction at a point midway between them is $\left({\mu }_0=4\pi \times {10}^{-7} \mathrm{H} {\mathrm{m}}^{-1}\right)$