A thin spherical insulating shell of radius R caries a uniformly distributed charge such that the potential act its surface is `V_(0)`. A hole with small area `alpha4piR^(2)(alpha lt lt 1)` is made in the shell without effecting the rest of the shell. Which one of the following is correct.

Options

A. The magnitude of `vecE` at a point located on a line passing through the hole and shell's centre on a distance 2R from the centre of spherical shell will be produced by `(alphaV_(0))/(2R)`
B. Potential at the centre of shell is reduced by `2alpha v 0`.
C. The magnitude of `vec(E)` at the centre of shell reduced by `(alphaV_(0))/(2R)`
D. The ratio of potential at the centre of the shell to that of the point at `1/2` R from centre towards the hole will be `(1-alpha)/(1-2alpha)`

Answer

D

Explanation

`dq=Q/(4piR^(2))dA=Qalpha`
Given
V at surface
`V_(0)=(KQ)/R`
V at C
`V_(C)=(KQ)/R-(KalphaQ)/R =V_(0) (1-alpha)`
V at B
`V_(B)=(KQ)/R -(K(alphaQ))/(R//2)=V_(0)(1-2alpha)`
`:. (V_(C))/(V_(B))=(1-alpha)/(1-2alpha)`
E at A
`E_(A)=(KQ)/((2R)^(2))-(KalphaQ)/(R^(2))=(KQ)/(4R^(2))-(alphaV_(0))/R`
So reduced by `(alphaV_(0))/R`
E at C
`E_(C)=(K(alphaQ))/(R^(2))=(alphaV_(0))/R`
So increasesd by `(alphaV_(0))/R`