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 α4πR2 (α<<1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct ?

Engineering

Physics

Electric Potential Energy and Electric Potential

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 α4πR² (α<<1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct ?

The potential at the center of the shell is reduced by 2αV₀

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 $\frac{{αV}_{0}}{2 R}$

The ratio of the potential at the center of the shell to that of the point at $\frac{1}{2}$ R from center towards the hole will be $\frac{1 - α}{1 - 2 α}$