### Electric Potential

There is no field inside the metal. In all points outside the metal the field is as if it is produced by a point charge $Q$ in the coordinate origin $r=0$: $\mathbf{E}=kQ\hat{\mathbf{r}}/r^2$ for $R_1 and $r>R_3$, and $\mathbf{E}=0$ for $r and $R_2.
The potential should be found by integrating
$\phi(r)= -\int_\infty^r E_r dr'=\left{\begin{matrix} kQ/r, & r\geq R_3\\ kQ/R_3, & R_2\leq r\leq R_3\\ kQ/R_3 +kQ/r-kQ/R_2, & R_1\leq r\leq R_2\\ kQ/R_3+kQ/R_1-kQ/R_2, & r\leq R_1 \end{matrix}\right. ^$