A particle of mass $‘m’$ and charge $‘q’$ is accelerated through a potential difference of $V$ volt, its energy will be

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

If $3$ charges are placed at the vertices of equilateral triangle of charge ‘$q$’ each. What is the net potential energy, if the side of equilateral triangle is $l\, cm$

A solid sphere of radius $R$ carries a charge $(Q+q)$ distributed uniformly over its volume. A very small point like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q.$ If it acquires a speed $v$ when it has fallen through a vertical height $y$ (see figure), then :

(assume the remaining portion to be spherical).

A proton of mass $m$ and charge $e$ is projected from a very large distance towards an $\alpha$-particle with velocity $v$. Initially $\alpha$-particle is at rest, but it is free to move. If gravity is neglected, then the minimum separation along the straight line of their motion will be

Two point charges $100\,\mu \,C$ and $5\,\mu \,C$ are placed at points $A$ and $B$ respectively with $AB = 40\,cm$. The work done by external force in displacing the charge $5\,\mu \,C$ from $B$ to $C$, where $BC = 30\,cm$, angle $ABC = \frac{\pi }{2}$ and $\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N{m^2}/{C^2}$.........$J$