$A$ spherically symmetric charge distribution is characterised by a charge density having the following variations:
$\rho (r) = \rho_0 \left( 1 - \frac{r}{R} \right)$ for $r < R$
$\rho (r) = 0$ for $r \ge R$
Where $r$ is the distance from the centre of the charge distribution and $\rho_0$ is a constant. The electric field at an internal point $(r < R)$ is:

  • A
    $\frac{\rho_0}{4\varepsilon_0} \left( \frac{r}{3} - \frac{r^2}{4R} \right)$
  • B
    $\frac{\rho_0}{\varepsilon_0} \left( \frac{r}{3} - \frac{r^2}{4R} \right)$
  • C
    $\frac{\rho_0}{3\varepsilon_0} \left( \frac{r}{3} - \frac{r^2}{4R} \right)$
  • D
    $\frac{\rho_0}{12\varepsilon_0} \left( \frac{r}{3} - \frac{r^2}{4R} \right)$

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