An infinite number of point charges, each carrying $1 \,\mu C$ charge, are placed along the y-axis at $y=1\, m , 2\, m , 4 \,m , 8\, m \ldots \ldots \ldots \ldots \ldots$

The total force on a $1 \,C$ point charge, placed at the origin, is $x \times 10^{3}\, N$. The value of $x$, to the nearest integer, is .........

[Take $\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,Nm ^{2} / C ^{2}\right]$

A conducting sphere of radius $R$, and carrying a charge $q$ is joined to a conducting sphere of radius $2R$, and carrying a charge $-2q$. The charge flowing between them will be

Two identical conducing spheres having unequal positive charges $q_1$ and $q_2$ separated by distance $r$. If they are made to touch each other and then separated again to the same distance. The electrostatic force between the spheres in this case will be (neglect induction of charges)

A given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force $F$. If the distance of the charge is doubled, the force acting on the charge will be

A paisa coin is made up of $\mathrm{Al - Mg}$ alloy and weighs $0.75\, g$ It is electrically neutral and contains equal amounts of positive and negative charge of magnitude $34.8$ $\mathrm{kC}$. Suppose that these equal charges were concentrated in two point charges separated by :

$(i)$ $1$ $\mathrm{cm}$ $(\sim \frac{1}{2} \times $ diagonal of the one paisa coin $)$

$(ii)$ $100\,\mathrm{m}$ $(\sim $ length of a long building $)$

$(iii)$ $10^6$ $\mathrm{m}$ (radius of the earth).

Find the force on each such point charge in each of the three cases. What do you conclude from these results ?

Two balls of same mass and carrying equal charge are hung from a fixed support of length $l$. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$ between the balls is proportional to