In the figure shown, a conducting sphere of inner radius $a$ and outer radius $b$ is given a charge $Q$. A point charge $q$ is placed in the cavity of this sphere at a distance $x \left(<a\right)$ away from the centre. Find the electric field intensity and electric potential at point $P$ (outside the sphere) at a distance $r \left(>b\right)$. Also, find the electric potential at the point $C$.

Both the ring and the conducting sphere are given the same charge $Q$. Determine the potential of the sphere. Assume that the centre of the sphere lies on the axis of the ring. Is it necessary that the charge on the ring be uniformly distributed to answer the above question?

A solid sphere of the radius $R$ has a cavity of radius $\frac{R}{2}.$ The solid part has a uniform charge density $\rho$ and cavity has no charge. Find the electric potential at the point $A$. Also, find the electric field (only magnitude) at a point $C$ inside the cavity.

Two identical thin rings each of radius $R$ meters are coaxially placed at a distance $R$ meters apart. If $Q_1$ coulomb and $Q_2$ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of other is