Charges of $2 \mu C$ and $-3 \mu C$ are placed at two points $A$ and $B$ separated by a distance of $1 \ m$. The distance of the point from $A$ where the net potential is zero is: (in $m$)

Consider a fixed uniformly charged insulating sphere with radius $R$ and total charge $+Q$. $A$ point charge $-q$ $(q \ll Q)$ with mass $m$ is released from rest at a distance of $3R$ from the centre of the charged sphere. When the point charge reaches the surface of the sphere, its speed is:
($\epsilon_0$ is the permittivity of vacuum, neglect gravitational forces).

$A$ non-conducting ring of radius $0.5\,m$ carries a total charge of $1.11 \times 10^{-10}\,C$ distributed non-uniformly on its circumference,producing an electric field $\vec{E}$ everywhere in space. The value of the line integral $\int_{l = \infty }^{l = 0} { - \vec{E} \cdot d\vec{l} }$ (where $l = 0$ is the centre of the ring) in volts is:

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 $......\,cm$.

An electron is accelerated through a potential difference of $2.5 \ V$. The energy gained by the electron is . . . . . . . (Charge of an electron = $1.6 \times 10^{-19} \ C$)

The potential difference $(V_A-V_B)$ in the arrangement shown in the figure is $(q=1 \mu C, x=2 \text{ cm}, y=3 \text{ cm})$.