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 $\alpha 4 \pi R ^2(\alpha<<1)$ is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?
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 $\alpha 4 \pi R ^2(\alpha<<1)$ is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?
- [IIT 2019]
- A
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 $\frac{1-\alpha}{1-2 \alpha}$
- B
The magnitude of electric field at the center of the shell is reduced by $\frac{\alpha V_0}{2 R}$
- C
The magnitude of electric field at a point, located on a line passing through the hole and shell's center on a distance $2 R$ from the center of the spherical shell will be reduced by $\frac{\alpha V_0}{2 R}$
- D
The potential at the center of the shell is reduced by $2 \alpha V _0$
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