$A$ total charge $q$ is divided into $q_1$ and $q_2$,which are placed at two vertices of an equilateral triangle of side $a$. The magnitude of the electric field $E$ at the third vertex of the triangle is to be depicted schematically as a function of $x = q_1 / q$. Choose the correct figure.

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?

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:

$A$ particle of mass $m$ and charge $q$ is thrown in a region where uniform gravitational field and electric field are present. The path of the particle:

An oil drop carries six electronic charges,has a mass of $1.6 \times 10^{-12} \text{ g}$ and falls with a terminal velocity in air. The magnitude of the vertical electric field required to make the drop move upward with the same speed as it was formerly moving is ........$kN/C$.

Two small conducting spheres of equal radius have charges of $10\ \mu C$ and $-20\ \mu C$ respectively and are placed at a distance $R$ from each other,experiencing a force $F_1$. If they are brought in contact and then separated to the same distance,the new force between them is $F_2$. Find the ratio $F_1 : F_2$.