$A$ ball of mass $1\, g$ and charge $10^{-8}\, C$ moves from a point $A$,where the potential is $600\, V$,to a point $B$,where the potential is $0\, V$. The velocity of the ball at point $B$ is $20\, cm/s$. The velocity of the ball at point $A$ will be:

Three charges each of value $+q$ are placed at the corners of an isosceles triangle $ABC$ with sides $AB = AC = 2a$. The midpoints of $AB$ and $AC$ are $D$ and $E$ respectively. The work done in taking a charge $Q$ from $D$ to $E$ is (where $\varepsilon_0$ is the permittivity of free space):

$A$ thin spherical shell is charged by some source. The potential difference between the two points $C$ (the center) and $P$ (a point on the surface) as shown in the figure is: (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}$)

The electric potentials at two points $P$ and $Q$ are $10 \ V$ and $-4 \ V$ respectively. The work done in moving $100$ electrons from $P$ to $Q$ is:

If $50 \, J$ of work must be done to move an electric charge of $2 \, C$ from a point,where potential is $-10 \, V$ to another point,where potential is $V \, V$,the value of $V$ is ......... $V$.

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