Question

A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at
its surface is V₀. A hole with a small area ????4????R₂ (????<<1) is made on the shell without affecting the rest of
the shell. Which one of the following statements is correct?
A. 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 center of the spherical shell will be reduced by ????V₀
2R
B. The magnitude of electric field at the center of the shell is reduced by ????V₀
2R
C. The ratio of the potential at the center of the shell to that of the point at 1 R from center towards the
2
hole will be 1 - ????
1 - 2????
D. The potential at the center of the shell is reduced by 2????V₀

Answer 1

Answer:

Given V at surface

V0​=RKQ​

V at C

VC​=RKQ​−RKαQ​=V0​(1−α)

V at B

VB​=RKQ​−R/2K(αQ)​=V0​(1−2α)

∴VB​VC​​=1−2α1−α​

E at A

EA​=(2R)2KQ​−R2KαQ​=4R2KQ​−RαV0​​

So reduced by RαV0​​

E at C

EC​=R2K(αQ)​=RαV0​​

So increased by RαV0​​.