Two identical charged spheres suspended from a common point by two massless strings of lengths $l$ are initially at a distance $d$ $(d << l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result,the spheres approach each other with a velocity $v$. Then $v$ varies as a function of the distance $x$ between the spheres,as:

Two equal negative charges are fixed at the points $(0, a)$ and $(0, -a)$ on the $y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $x$-axis. The charge $Q$ will

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 conducting spheres $A$ and $B$ carry equal charge. They are separated by a distance much larger than their diameter,and the force between them is $F$. $A$ third identical conducting sphere,$C$,is uncharged. Sphere $C$ is first touched to $A$,then to $B$,and then removed. As a result,the force between $A$ and $B$ would be equal to

The electric field is in the direction of the $x$-axis. The work done to move a charge of $0.2 \ C$ by a distance of $2 \ m$ at an angle of $60^\circ$ with the $x$-axis is $4 \ J$. What is the value of the electric field $E$ in $N/C$?

Answer the following:
$(a)$ The top of the atmosphere is at about $400 \; kV$ with respect to the surface of the earth,corresponding to an electric field that decreases with altitude. Near the surface of the earth,the field is about $100 \; Vm^{-1}$. Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)
$(b)$ $A$ man fixes outside his house one evening a two-metre-high insulating slab carrying on its top a large aluminium sheet of area $1 \; m^2$. Will he get an electric shock if he touches the metal sheet next morning?
$(c)$ The discharging current in the atmosphere due to the small conductivity of air is known to be $1800 \; A$ on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words,what keeps the atmosphere charged?
$(d)$ What are the forms of energy into which the electrical energy of the atmosphere is dissipated during lightning?