An infinite number of charges,each of charge $1 \,\mu C$,are placed on the $x$-axis at coordinates $x = 1, 2, 4, 8, ... \infty$. If a charge of $1 \, C$ is kept at the origin,what is the net force acting on the $1 \, C$ charge in Newtons?

Two small spherical balls,each carrying a charge $Q = 10\,\mu C$ ($10$ micro-coulomb),are suspended by two insulating threads of equal lengths $1\,m$ each,from a point fixed in the ceiling. It is found that in equilibrium,the threads are separated by an angle of $60^o$ between them,as shown in the figure. What is the tension in the threads in $N$? (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9\,Nm^2/C^2$)

$A$ charge $Q$ is divided into two parts $q$ and $Q - q$. If the Coulomb repulsion between them when they are separated by a distance $r$ is to be maximum,the ratio of $\frac{Q}{q}$ should be:

In the common crystal structure of $CsCl$,$Cs^+$ and $Cl^-$ ions are arranged in a $bcc$ structure as shown in the figure. The net electrostatic force on the $Cl^-$ ion due to the eight $Cs^+$ ions is .......

Three charged particles of each mass $0.1 \,g$ and charge $q$ are suspended from a common rigid point by insulated massless threads of each $1 \,m$ long. If the three particles are in equilibrium and are located at the corners of an equilateral triangle of side $3 \,cm$, the charge $q$ on each particle is . . . . . . $nC$. (The angle made by the line joining the centroid of the triangle and the point of suspension with the vertical is very small). (Acceleration due to gravity $= 10 \,ms^{-2}$ and $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \,Nm^2 C^{-2}$)

Two charges $+q$ and $-3q$ are placed on the $x$-axis separated by a distance $d$. ($-3q$ is to the right of $q$). Where should a third charge $2q$ be placed such that it will not experience any net force?