A thin spherical insulating shell of radius carries a uniformly distributed charge…

PHYSICS · Single correct · AP · Physics C: Electricity and Magnetism · Electric Charges Fields and Gauss's Law · Electric Charges Fields and Gauss's Law

Problem

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

\alpha 4\pi R^2

(

a \ll 1

) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct? [Adv. 2019] (1) The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance

2R

from the centre of the spherical shell will be reduced by

\frac{\alpha V_0}{2R}

(2) The ratio of the potential at the centre of the shell to that of the point at

\frac{1}{2}R

from the centre towards the hole will be

\frac{1-\alpha}{1-2\alpha}

(3) The magnitude of electric field at the centre of the shell is reduced by

\frac{\alpha V_0}{2R}

(4) The potential at the centre of the shell is reduced by

2\alpha V_0

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