Two identical magnetic dipoles of magnetic moments $1.0 {\mathrm{Am}}^2$ each, are placed at a separation of 2m with their axis perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is 

With respect to $1^{\mathrm{st}}$ magnet, P lies in end side-on position.

$\therefore {\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\left(\frac{2\mathrm{M}}{{\mathrm{d}}^3}\right)\left(\mathrm{RHS}\right)$

With respect to $2^{\mathrm{nd}}$ magnet, P lies in broad side - on position.

$\therefore {\mathrm{B}}_2=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\left(\frac{\mathrm{M}}{{\mathrm{d}}^3}\right)\left(\mathrm{Upward}\right)$

${\mathrm{B}}_1={10}^{-7} \mathrm{x} \frac{2 \mathrm{x} 1}{1}=2 \mathrm{x} {10}^{-7} \mathrm{T}, {\mathrm{B}}_2=\frac{{\mathrm{B}}_1}{2}={10}^{-7} \mathrm{T}$

As ${\mathrm{B}}_1 \mathrm{and} {\mathrm{B}}_2$ are mutually perpendicular, hence the resultant magnetic field is

${\mathrm{B}}_{\mathrm{R}}=\sqrt{{{\mathrm{B}}_1}^2+{{\mathrm{B}}_2}^2}=\sqrt{{\left(2 \mathrm{x} {10}^{-7}\right)}^2+{\left({10}^{-7}\right)}^2}$

$=\sqrt{5} \mathrm{x} {10}^{-7} \mathrm{T}$