A charge of ${10^{ – 9}}\,C$ is placed on each of the $64$ identical drops of radius $2\,cm$. They are then combined to form a bigger drop. Find its potential

A charge $ + q$ is fixed at each of the points $x = {x_0},\,x = 3{x_0},\,x = 5{x_0}$….. $\infty$, on the $x – $axis and a charge $ – q$ is fixed at each of the points $x = 2{x_0},\,x = 4{x_0},x = 6{x_0}$,….. $\infty$. Here ${x_0}$ is a positive constant. Take the electric potential at a point due to a charge $Q$ at a distance $r$ from it to be $Q/(4\pi {\varepsilon _0}r)$. Then, the potential at the origin due to the above system of charges is

Consider two conducting spheres of radii ${{\rm{R}}_1}$ and ${{\rm{R}}_2}$ with $\left( {{{\rm{R}}_1} > {{\rm{R}}_2}} \right)$. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. On bringing them in contact there is