A short bar magnet with its north pole facing geographic north forms a neutral point at P in the horizontal plane. If the magnet is rotated by ${90}^{\mathrm{o}}$ in the horizontal plane, the net magnetic induction at P is (Horizontal component of earth's magnetic field = ${\mathrm{B}}_{\mathrm{H}}$)

Initially, 

Neutral point is obtained on equatorial line and at neutral point $\left|{\mathrm{B}}_{\mathrm{H}}\right|=\left|{\mathrm{B}}_{\mathrm{e}}\right|$

where ${\mathrm{B}}_{\mathrm{H}}$= Horizontai component of earth's magnetic field, ${\mathrm{B}}_{\mathrm{e}}$= Magnetic field due to bar magnet on its equatorial line 

Finally, 

Point P comes on axial line of the magnet and at P, 

Net magnetic field $\mathrm{B}=\sqrt{{{\mathrm{B}}_{\mathrm{a}}}^2+{{\mathrm{B}}_{\mathrm{H}}}^2}$

$=\sqrt{{\left(2{\mathrm{B}}_{\mathrm{e}}\right)}^2+{\left({\mathrm{B}}_{\mathrm{H}}\right)}^2}=\sqrt{{\left(2{\mathrm{B}}_{\mathrm{H}}\right)}^2+{{\mathrm{B}}^2}_{\mathrm{H}}}=\sqrt{5}{\mathrm{B}}_{\mathrm{H}}$