A thin-walled spherical conducting shell \( S \) of radius \( R \) is given charge \( Q \). The ...

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A thin-walled spherical conducting shell \( S \) of radius \( R \) is given charge \( Q \). The same amount of charge is also placed at its center \( C \). Which of the following statements are correct?
(1) On the outer surface of \( S \), the charge density is \( Q / 2 \pi R^{2} \).
(2) The electric field is zero at all points inside \( S \).
(3) At a point just outside \( S \), the electric field is double the field at a point just inside \( S \) in the cavity.
(4) At any point inside \( S \) (i.e., within its cavity), the electric field is inversely proportional to the square of its distance from \( C \).
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