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?

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

The electric field is Zero at all points inside S

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

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

answer is C, D, A.

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Detailed Solution

As a charge Q is placed at center there will be induced charge -Q at inner surface of sphere. hence charge a charge of additional Q is induced on the outer surface of the spherical shell.

$⇒charge density \frac{2 Q}{4 π r^{2}} = \frac{Q}{2 π r^{2}}$

Just outside S, the charge and shell will act as a 2Q charge placed at C, therefore the field will be double that of just inside the shell.

At any point inside S, the electric field is only due to the charge Q placed at C, hence the electric field is inversely proportional to the square of its distance from C

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