A point electric dipole with dipole moment ‘P’ is placed in the external uniform electric field whose strength is ‘E₀’ with $\overrightarrow{\mathrm{P}}$ parallel to ‘E₀’. Then

Since the dipole is placed in uniform electric field , net force experienced by the dipole is zero.

Consider a point  at a radial distance r , whose position vector makes an angle $\mathrm{\theta } \mathrm{with} \overrightarrow{\mathrm{p}}.$If the point lies on a spherical equipotential surface with its centre at the centre of the dipole , then tangential component of electric field at P must be zero. 

Therefore , $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{\mathrm{P} \sin \mathrm{\theta }}{{\mathrm{r}}^3} -{\mathrm{E}}_0\sin \mathrm{\theta } = 0 \Rightarrow \mathrm{r} = {\left(\frac{\mathrm{P}}{4{\mathrm{\pi \epsilon }}_0 {\mathrm{E}}_0}\right)}^{\frac{1}{3}}$