Point charges are placed at the vertices of a regular hexagon with center $O$ and side length $L$ as shown in the figure. Given $K = \frac{q}{4\pi \epsilon_0 L^2}$,which of the following statements is correct?

Two identical small spheres carry charges $Q_1$ and $Q_2$ $(Q_1 >> Q_2)$. The force between them is $F_1$. The spheres are brought into contact and then placed at the same distance. The new force between them is $F_2$. Then $F_1/F_2$ will be:

Two free point charges $+q$ and $+4q$ are a distance $R$ apart. $A$ third charge is so placed that the entire system is in equilibrium. Then the third charge is :-

Let $E_1(r)$,$E_2(r)$,and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$,an infinitely long wire with constant linear charge density $\lambda$,and an infinite plane with uniform surface charge density $\sigma$. If $E_1(r_0) = E_2(r_0) = E_3(r_0)$ at a given distance $r_0$,then:

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 point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of a $(X, Y)$ coordinate system. Then: