The electric field due to a small electric dipole at a distance $r$  from its centre in axial position is E. If the dipole is rotated through an angle of ${90}^0$  about its perpendicular axis, the electric field at the same point will be

After rotation, the same point becomes a point on equatorial line.

So initially at axial point, the magnitude of electric field ${\mathrm{E}}_{\mathrm{axial}}=\frac{\mathrm{K}2\mathrm{P}}{{\mathrm{r}}^3}$

After rotating, the field at an equatorial point the magnitude of electric field ${\mathrm{E}}_{\mathrm{equi}}=\frac{\mathrm{KP}}{{\mathrm{r}}^3}=\frac{{\mathrm{E}}_{\mathrm{axial}}}{2}$