A point chargr $Q$ is fixed A small charge $q$ and mass $m$ is given a velocity $v_0$ from infinity & perpendicular distance $r_0$ as shown. If distance of closest approach is $r_0/2$. The value of $q$ is [Given $mv_0^2 = \frac{{{Q^2}}}{{4\pi { \in _0}\,{r_0}}}$]

Two positrons $(e^+)$ and two protons $(p)$ are kept on four corners of a square of side $a$ as shown in figure. The mass of proton is much larger than the mass of positron. Let $q$ denotes the charge on the proton as well as the positron then the kinetic energies of one of the positrons and one of the protons respectively after a very long time will be-

Nine point charges are placed on a cube as shown in the figure. The charge $q$ is placed at the body centre whereas all other charges are at the vertices. The electrostatic potential energy of the system will be

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 equal charges $q$ are placed at a distance of $2a$ and a third charge $ - 2q$ is placed at the midpoint. The potential energy of the system is

A positively charged ring is in $y-z$ plane with its centre at origin. A positive test charge $q_0$, held at origin is released along $x$-axis, then its speed