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?

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The electric field is zero at all points inside S.

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

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

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

answer is A, C, D.

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Detailed Solution

Due to induction there will be a charge of -Q on the inner surface of the shell, So there will be an additional charge of +Q on the outer surface other than the charge placed.

Surface charge density is given by $σ = \frac{2 Q}{4 {πr}^{2}} = \frac{Q}{2 {πr}^{2}}$

For a point just below the surface of the shell the electric field is just because of the point charge, but for any point above the surface of the shell the electric field will be due to the point charge and also the shell.

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

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