$A$ spherically symmetric charge distribution is characterized by a charge density $\rho(r) = \rho_0 \left( \frac{5}{4} - \frac{r}{R} \right)$ for $r \le R$ and $\rho(r) = 0$ for $r > R$,where $r$ is the distance from the origin. The electric field at a distance $r$ from the origin $(r < R)$ is given by:

  • A
    $\frac{\rho_0 r}{3\varepsilon_0} \left( \frac{5}{4} - \frac{r}{R} \right)$
  • B
    $\frac{\rho_0 r}{3\varepsilon_0} \left( \frac{5}{4} - \frac{3r}{4R} \right)$
  • C
    $\frac{\rho_0 r}{4\varepsilon_0} \left( \frac{5}{3} - \frac{r}{R} \right)$
  • D
    $\frac{4\rho_0 r}{3\varepsilon_0} \left( \frac{5}{4} - \frac{r}{R} \right)$

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