A thin spherical insulating shell of radius carries a uniformly distributed charge such that the potential at its surface is . A hole with a small area is made in the shell without affecting the rest of the shell. Which one of the following is correct.
The ratio of potential at the centre of the shell to that of the point at from the centre toward the hole will be
The explanation for the correct option(s):
Option D: The ratio of potential at the center of the shell to that of the point at from the center towards the hole will be
We know that the potential at a surface is given as,
Where, is a constant equal to
is the radius of the hole
is the charge on the sphere
is the radius of the sphere
And also the potential at the centre will be,
…….
Potential at the point B will be,
……..
Taking the ratio between the equation and then,
Hence, The ratio of potential at the center of the shell is
The explanation for the incorrect option(s):
Option A: The magnitude of at a point located on a line passing through the hole and shell’s centre at a distance from the centre of the spherical shell will be reduced by
The electric field experienced at is given as,
The electric field at is increasing by.
Option B: Potential at the centre of the shell is reduced by
The potential at the centre will be,
Option C: The magnitude of at the centre of the shell is reduced by
The electric field acting at the point is,
The electric field will be reduced by
Therefore, the ratio of potential at the centre of the shell to that of the point at from the centre towards the hole will be
Hence, Option 'D' is Correct.