Two short magnets of equal dipole moments M are fastened perpendicularly at their centre (see figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is.

 

Resultant magnetic moment of the two magnets is

${\text{M}}_{\text{net}}\text{=}\sqrt{{\text{M}}^{\text{2}}{\text{+\hspace{0.17em}M}}^{\text{2}}}\text{\hspace{0.17em}=\hspace{0.17em}}\sqrt{\text{2}}\times \text{\hspace{0.17em}M}$

Imagine a short magnet lying along OP with magnetic moment equal to $\text{M}\sqrt{\text{2}}$. Thus point P lies on the axial line of the magnet.
$\therefore$Magnitude of magnetic field at P is given by $\text{B\hspace{0.17em}=}\frac{{\text{μ}}_{\text{0}}}{\text{4π}}\text{\hspace{0.17em}\hspace{0.17em}.\hspace{0.17em}\hspace{0.17em}}\frac{\text{2}\sqrt{\text{2}}\text{\hspace{0.17em}M}}{{\text{d}}^{\text{3}}}$