Two identical charges $+Q$ are kept fixed at some distance apart. $A$ small particle $P$ with charge $q$ is placed midway between them. If $P$ is given a small displacement $\Delta$,it will undergo simple harmonic motion if:

Two equal negative charges $-q$ each 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 :-

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?

$A$ uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to

Suppose the charge of a proton and an electron differ slightly. One of them is $-e,$ the other is $(e + \Delta e).$ If the net electrostatic force and gravitational force between two hydrogen atoms placed at a distance $d$ (much greater than atomic size) apart is zero, then $\Delta e$ is of the order of $[$ Given: mass of hydrogen $m_h = 1.67 \times 10^{-27} \, kg]$

For two electrons separated by a distance of $10 \, cm$,let $F_g$ and $F_e$ represent the gravitational force and electrostatic force between them,respectively. The ratio $F_g / F_e$ is of the order of: