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The static electric field inside a dielectric medium with relative permittivity,

$\varepsilon _{r}=2.25$, expressed in cylindrical coordinate system is given by the following


$$E=a_{r}2r+a_{\varphi }\left ( \frac{3}{r} \right )+a_{z}6$$

where $a_{r},a_{\varphi },a_{z}$ are unit vectors along $\text{r, $\varphi$ and 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, $\varepsilon _{0}$ in $\text{SI}$ units is given by:

  1. $3\varepsilon _{0}$
  2. $4\varepsilon _{0}$
  3. $5\varepsilon _{0}$
  4. $9\varepsilon _{0}$
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