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 \( O P=a=R_{1}-R_{2} \) (see figure) is made. If the electric field inside the cavity at position \( \vec{r} \) is \( \vec{E}(\vec{r}) \), then the correct statement(s) is(are)
(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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