A dipole having dipole moment p is placed in front of a solid neutral conducting sphere as shown in figure. The net potential at point A on the surface of sphere is:

Electric potential due to a electric dipole is given by 

$\mathrm{V}=\frac{\mathrm{k} \overrightarrow{\mathrm{P}}.\overrightarrow{\mathrm{r}}}{{\mathrm{r}}^3}$

The potential at the centre of the sphere is given by

$\mathrm{V}=\frac{\mathrm{kP}\left(\frac{\mathrm{r}}{\mathrm{cos\varphi }}\right)}{{\left(\frac{\mathrm{r}}{\mathrm{cos\varphi }}\right)}^3}=\frac{{\mathrm{kPcos}}^2\mathrm{\varphi }}{{\mathrm{r}}^2}$

As the sphere is conducting in nature the potential at point O = potential at point A.