A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V_0. A hole with a small area 4 R^2 ( 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

JEE Advanced 2019 Physics question

A thin spherical insulating shell of radius carries a uniformly distributed charge such that the potential at its surface is . A hole with a small area () is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

(A)The potential at the center of the shell is reduced by
(B)The magnitude of electric field at the center of the shell is reduced by
(C)The ratio of the potential at the center of the shell to that of the point at from center towards the hole will be Correct
(D)The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance from the center of the spherical shell will be reduced by

Answer: (C)

Solution

Let the shell carry charge , so . The shell with a hole = complete shell + a small patch of charge at the hole (a point charge, since ). Centre: , i.e. reduced by , so (A) is wrong. Point at towards the hole

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Question ID VK-026809