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 \alpha4\piR^2(\alpha < < 1) is made on the shell without affecting the rest of the shell. Which one of the following statement(s) is correct? [JEE Adv 2019 P1]

Correct Answer is : The ratio of the potential at the centre of the shell to that of the point at 12R from centre towards the hole will be 1−α2−α

The magnitude of electric field at the centre of the shell is reduced by \frac{\alphaV_0}{2R}

The ratio of the potential at the centre of the shell to that of the point at 1/2R from centre towards the hole will be \frac{1-\alpha}{2-\alpha}

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{\alphaV_0}{2R}

The potential at the center of the shell is reduced by 2 aV_0

Electrostatics

Section: Physics

Question : 21 of 59

Marks: +1, -0

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 statement(s) is correct?

[JEE Adv 2019 P1]

The magnitude of electric field at the centre of the shell is reduced by
αV0
2R
The ratio of the potential at the centre of the shell to that of the point at
1
2
R from centre towards the hole will be
1−α
2−α
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
αV0
2R
The potential at the center of the shell is reduced by 2aV0

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