Question

Pick the correct statement –
           

A) Charge on the surface of the inner sphere is non-uniformly distributed.
B) Charge on inner surface of outer shells is non-uniformly distributed
C) Charge on the outer surface of the outer shell is non-uniformly distributed.
D) All the above are false.

Answer 1

Hint: We need to find the charge distribution pattern on the outer and inner shell of the given spherical shell. It is influenced by a charge outside the sphere. Also, we need to consider the earthing involved in the spherical inner shell.

Complete answer:
We are given a spherical shell with two surfaces of radii ‘a’ and ‘2a’ respectively. A charge ‘q’ is placed at a distance from the spherical shell which influences the charge distribution of the shell.
                       

We can see that all the points on the two shells of spherical shape are equidistant from the centre, but the charge is not inside the shell, therefore, the charge distribution is not uniform on the surface.
The inner shell is earthed. The electric field influence on the inner shell is balanced by this earthing and therefore, has a uniform charge distribution on it.
The outer shell has the charge ‘q’ at a distance which is not equidistant from the different points on the surface. The surface perpendicular and close to the charge has a higher charge as related to the opposite point on the sphere.
From the above observation, we understand that the inner shell has a uniform charge distribution and the outer spherical shell doesn’t possess a uniform charge distribution.

The correct answer is option C.

Note:
The inner surface of the inner shell doesn’t have any charge distribution as similar to the outer surface of the inner shell. For the outer shell, the inner surface doesn’t have any charge distribution as it is the case for spherical shells of conducting materials.