Two small conducting balls of identical mass $20 \text{ g}$ and identical charge $10^{-10} \text{ C}$ hang from non-conducting threads of length $L = 300 \text{ cm}$. If the equilibrium separation of the balls is $x$ and $x \ll L$,then the magnitude of $x$ is (Assume $4 \pi \varepsilon_0 = \frac{1}{9 \times 10^9} \text{ F/m}$ and $g = 10 \text{ m/s}^2$):

Consider the charges $q, q$,and $-q$ placed at the vertices of an equilateral triangle of side $l$,as shown in the figure. What is the force on each charge?

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is

Find the value of $q$ so that the net electrostatic force on the $10 \mu C$ charge placed at a vertex of the square is zero. The charges are arranged as shown in the figure.

$A$ proton and an anti-proton come close to each other in vacuum such that the distance between them is $10 \, cm$. Consider the potential energy to be zero at infinity. The velocity at this distance will be ........... $\, m/s$.

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 $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \,Nm^2 C^{-2}$)