Small identical balls with equal charges are fixed at the vertices of a regular polygon of $N$ sides, each of length $d$. At a certain instant, one of the balls is released. After a long time interval, the adjacent ball to the previous one is released. The difference in kinetic energies of the two released balls is $K$, at a sufficiently long distance from the polygon.

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.