A point charge q is placed at a distance $\mathcal{l}$ from centre of an uncharged conducting sphere of radius $r(\mathcal{l}>>r)$

 

Induced surface charge density $\sigma$ as a function of $\theta$ is given by $\frac{q\cos \theta }{4\pi {\mathcal{l}}^2}$

Induced surface charge density $\sigma$ as a function of $\theta$ is given by $\frac{3q\cos \theta }{4\pi {\mathcal{l}}^2}$

Induced dipole moment of sphere is given by $\frac{q{r}^3}{{\mathcal{l}}^2}$

Induced dipole moment of sphere is given by $\frac{2q{r}^3}{{\mathcal{l}}^2}$