Two identical short bar magnets, each having magnetic moment of  $10A{M}^2$, 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 m, the resultant magnetic induction at a point midway between them is $({\mu }_0=4\pi \times {10}^{-7}H{m}^{-1})$ .  $\sqrt{f}x{10}^{-3}T$. Find f.