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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 centre $C. $ Which of the following statements are correct ?
On the outer surface of $S$, the charge density is $\frac{Q}{{2\pi {R^2}}}$.
At any point inside $S$, the electric field is inversely proportional to the square of its distance from $C$.
At a point just outside $S,$ the electric field is double the field at a point just inside $S.$
all of the above
Solution
because of charge $Q$ at center there will be induced $charge-Q$ at inner surface of sphere.
hence charge density $\frac{2 Q}{4 \pi r^{2}}=\frac{Q}{2 \pi r^{2}}$
because of $2 Q$ charge outside the electric field is double that of inside.
At any point inside $S$, the electric field is inversely proportional to the square of its distance from $C$
