[UPSC IFoS 2025] Electrostatics and Magnetostatics (Q15, 10M)

If volume charge density in free space varies as \rho_{\text{v}} = \frac{100\varepsilon_0}{\text{r}^{2/5}}, then using Poisson's equation, find potential \text{V}(\text{r}). It is assumed that \text{r}^2 \text{E}_{\text{r}} \rightarrow 0 when \text{r} \rightarrow 0, while \text{V} \rightarrow 0 at \text{r} \rightarrow \infty.