A ball of charge q is placed in a hollow conducting uncharged sphere. After this, the sphere is connected with earth for a short time and the ball is then removed from the sphere. The ball has not been brought into contact with the sphere.
a. What charge will the sphere have after these operations? Where and how will this charge be distributed?
b. What will be the electric field inside as well as outside the sphere?

Explanation

a.i. When we bring a charge q at the centre of a sphere,
charges `-q` and `+q` will be induced on inner surface
and outer surface, respectively, as shown in figure.

ii. After earthing , +q will be transferred to earth as
shown in figure.
iii. After removing the earthing and charge q from
centre, -q will be distributed uniformly on the
external surface of the sphere as shown in figure.
So finally the sphere will have charge -q
distributed uniformly on the external surface.
b. The intensity of the electric field inside the sphere
will be zero. An electric field similar to the field
of the point charge q situated at the centre of the
sphere will be set up outside the sphere. Direction
of the field will be radially inward.