GATE Electrical Engineering (EE) 2020 Solved Paper

The static electric field inside a dielectric medium with relative permittivity, ${\mathit{\epsilon }}_{\mathit{r}}=2.25$, expressed in cylindrical coordinate system is given by the following expression $$\mathit{E}={\mathit{a}}_{\mathit{r}}2\mathit{r}+{\mathit{a}}_{\mathit{\phi }}\left(\frac{3}{\mathit{r}}\right)+{\mathit{a}}_{\mathit{z}}6$$ Where ${\mathit{a}}_{\mathit{r}},{\mathit{a}}_{\mathit{\varphi },}{\mathit{a}}_{\mathit{z}}$ are unit vectors along $\mathit{r},\mathit{\varphi }$ and $\mathit{z}$ directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittivity, ${\mathit{\epsilon }}_0$, in SI unit is given by: