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)

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

A uniform electric field, $\overrightarrow{E}=-400\sqrt{3} \hat{\mathrm{j}} \mathrm{N} {\mathrm{C}}^{-1}$ is applied in a region. A charged particle of mass $m$ carrying positive charge $q$ is projected in this region with an initial speed of $2\sqrt{10}\times {10}^6 \mathrm{m} {\mathrm{s}}^{-1}$. This particle is aimed to hit a target $T$, which is $5 \mathrm{m}$ away from its entry point into the field as shown schematically in the figure. Take $\frac{q}{m}={10}^{10} \mathrm{C} {\mathrm{kg}}^{-1}$. Then