Consider a uniform spherical charge distribution of radius  $R_1$ centred at the origin O.  In this distribution, a spherical cavity of radius  $R_2$, centred at  P with distance  $OP=a=R_1-R_2$ (see figure) is made.  If the electric field inside the cavity at position  $\overrightarrow{r}$ is  $\overrightarrow{E}\left(\overrightarrow{r}\right)$, then the correct statement(s) is (are)

The sphere with cavity can be assumed as a complete sphere with +ve charge, radius  $R_1$ + another complete sphere with –ve charge, radius $R_2$ .

Inside a spherical charge distribution for an internal point $\overrightarrow{E}=\frac{\rho }{3{\epsilon }_0}\overrightarrow{r}$         

$E_{+}\to E$ due to total +ve charges                             

$E_{-}\to E$  due to total $-ve$  charges  

Electric filed at any point inside cavity is given by,

$$\begin{gathered} \stackrel{ }{\overrightarrow{E}}={\stackrel{ }{\overrightarrow{E}}}_{+}+{\stackrel{ }{\overrightarrow{E}}}_{-} \\ \Rightarrow \overrightarrow{E}=\frac{\rho }{3{\epsilon }_0}\overrightarrow{r_1}+\frac{\left(-\rho \right)}{3{\epsilon }_0}\overrightarrow{r_2}=\frac{\rho }{3{\epsilon }_0}\left(\overrightarrow{r_1}-\overrightarrow{r_2}\right)=\frac{\rho }{3{\epsilon }_0}\overrightarrow{a} \end{gathered}$$                      

$\overrightarrow{E}$  is uniform and both its magnitude and direction depend on  $\overrightarrow{a}$