A thin spherical indulating 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 ratio of potential at the centre of the shell to that of the point at `(1)/(2)` R from center towards the hole will be `(1-alpha)/(1-2alpha)`
B. The magnitude of electric field at the center of the shell is reduced by `(alphaV_(0))/(2R)`
C. 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 `(alphaV_(0))/(2R)`
D. The potential at the center of shell is reduced by `2alpha v_(0)`.

Answer

A