Two small spheres,each having an equal positive charge $Q$ (Coulomb),are suspended by two insulating strings of equal length $L$ (metre) from a rigid hook. The whole setup is taken into a satellite where there is no gravity. The two balls are now held by electrostatic forces in a horizontal position. The tension in each string is then:

Two point charges of $+2 \, \mu \text{C}$ and $+6 \, \mu \text{C}$ repel each other with a force of $12 \, \text{N}$. If a charge of $-4 \, \mu \text{C}$ is added to each,the force will be:

Two particles of equal mass $m$ and charge $q$ are placed at a distance of $16 \, cm$. They do not experience any net force. The value of $\frac{q}{m}$ is

Two spheres having the same radius and mass are suspended by two strings of equal length from the same point in such a way that their surfaces touch each other. On depositing a charge of $2 \times 10^{-6} \ C$ on them,they repel each other such that in equilibrium,the angle between their strings becomes $60^{\circ}$. If the distance from the point of suspension to the center of the sphere is $10 \ cm$,find the mass of each sphere. $(k = 9 \times 10^9 \ SI, g = 10 \ ms^{-2})$. (in $kg$)

The force between two charges of $+3 \ \mu C$ and $+8 \ \mu C$ is $40 \ N$. If a charge of $-5 \ \mu C$ is added to both,what will be the new force in $N$?

$A$ paisa coin is made up of $Al-Mg$ alloy and weighs $0.75\,g$. It is electrically neutral and contains equal amounts of positive and negative charge of magnitude $34.8\,kC$. Suppose that these equal charges were concentrated in two point charges separated by:
$(i)$ $1\,cm$ $(\sim \frac{1}{2} \times \text{diagonal of the one paisa coin})$
$(ii)$ $100\,m$ $(\sim \text{length of a long building})$
$(iii)$ $10^6\,m$ $(\text{radius of the earth})$.
Find the force on each such point charge in each of the three cases. What do you conclude from these results?