Two protons are separated by a distance of $10^{-10} \ m$. If they are released,what will be their total kinetic energy at an infinite distance?

Under the influence of the Coulomb field of charge $+Q$,a charge $-q$ is moving around it in an elliptical orbit. Find out the correct statement$(s)$.

$A$ point charge $q$ moves from point $P$ to $S$ along the path $PQRS$ in a uniform electric field $E$ directed parallel to the positive $X$-axis. The coordinates of points $P, Q, R,$ and $S$ are $(a, b, 0), (2a, 0, 0), (a, -b, 0),$ and $(0, 0, 0)$ respectively. Calculate the work done by the electric field in this process.

Consider a gravity-free container as shown. The system is initially at rest and the electric potential in the region is $V = (y^3 + 2) \text{ J/C}$. A ball of charge $q = -0.5 \text{ C}$ and mass $m = 2 \text{ kg}$ is released from rest from the base $(y=0)$. It starts to move up due to the electric field and collides with the shaded top face $(y=2 \text{ m})$ as shown. If its speed just after the collision is $1.5 \text{ m/s}$ and the time for which the ball is in contact with the shaded face is $0.1 \text{ s}$, find the external force required to hold the container fixed in its position during the collision, assuming the ball exerts a constant force on the wall during the entire span of the collision. (in $\text{ N}$)

How much work is done in moving a charge $+q$ once around a circle of radius $r$ in the presence of a central charge $+Q$?

In the given figure,two tiny conducting balls of identical mass $m$ and identical charge $q$ hang from non-conducting threads of equal length $L$. Assume that $\theta$ is so small that $\tan \theta \approx \sin \theta$,then for equilibrium,$x$ is equal to: