A thin-walled, spherical conducting shell $S$ of radius $R$ is given charge $Q$. The same amount of charge is also placed at its centre $C. $ Which of the following statements are correct ? 

  • A

    On the outer surface of $S$, the charge density is $\frac{Q}{{2\pi {R^2}}}$.

  • B

    At any point inside $S$, the electric field is inversely proportional to the square of its distance from $C$.

  • C

    At a point just outside $S,$ the electric field is double the field at a point just inside $S.$

  • D

    all of the above

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  • [KVPY 2017]