Three concentric spherical metallic shells $X , Y$ and $Z$ of radius $a , b$ and c respectively $[ a < b < c ]$ have surface charge densities $\sigma,-\sigma$ and $\sigma$, respectively. The shells $X$ and $Z$ are at same potential. If the radii of $X$ and $Y$ are $2\,cm$ and $3\,cm$, respectively.The radius of shell $Z$ is $......cm$.

Write an equation for potential due to volume charge distribution.

A thin spherical shell is charged by some source. The potential difference between the two points $C$ and $P$ (in $V$) shown in the figure is:

(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ $SI$ units)

Concentric metallic hollow spheres of radii $R$ and $4 R$ hold charges $Q _{1}$ and $Q _{2}$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V ( R )- V (4 R )$ is

Three charges $2 q,-q$ and $-q$ are located at the vertices of an equilateral triangle. At the center of the triangle

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