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?

Two identical metal spheres charged with $+12 \mu C$ and $-8 \mu C$ are kept at a certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is (in $: 1$)

In $1959$,Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$,which is maintained constant. Let the charge on the proton be: $e_p = -(1 + y)e$,where $e$ is the electronic charge.
$(a)$ Find the critical value of $y$ such that expansion may start.
$(b)$ Show that the velocity of expansion is proportional to the distance from the centre.

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges repel each other with a force $F$ when kept apart at some distance. $A$ third spherical conductor $A$ having the same radius as that of $B$ but uncharged,is brought in contact with $B$,then brought in contact with $C$,and finally removed away from both. The new force of repulsion between $B$ and $C$ is-

The diagram shows three infinitely long uniform line charges placed on the $X, Y$ and $Z$ axes with linear charge densities $2\lambda, 3\lambda$ and $\lambda$ respectively. The work done by an external agent in moving a unit positive charge from $(1, 1, 1)$ to $(0, 1, 1)$ is equal to:

Two equal charges $q$ are placed at a distance of $2a$ on the $x$-axis. A third charge $q$ of mass $m$ is placed at the midpoint between them. If this charge is displaced by a small distance $x$ from the equilibrium position, the particle will: