Consider a uniform spenerical charge distribution of radius $\mathrm{R}_1$ centred at the origin O . In this distribution, a spherical cavity of radius $R_2$, centred at $P$ with distance $O P=a=R_1-R_2$ (see figure) is made. If the electric field inside the cavity at position $\overrightarrow{\mathrm{r}}$ is $\overrightarrow{\mathrm{E}}(\overrightarrow{\mathrm{r}})$, then the correct statement(s) is(are)
Select the correct option:
A
$\vec{E}$ is uniform, its magnitude is independent of $R_2$ but its direction depends on $\vec{r}$
B
$\vec{E}$ is uniform, its magnitude independs of $R_2$ and its direction depends on $\vec{r}$
C
$\vec{E}$ is uniform, its magnitude is independent of a but its direction depends on $\vec{a}$
D
$\vec{E}$ is uniform, and both its magnitude and direction depends on $\vec{a}$
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