Two small conducting spheres of equal radius have charges $+10\,\mu C$ and $-20\,\mu C$ respectively and are placed at a distance $R$ from each other,experiencing a force $F_1$. If they are brought into contact and then separated to the same distance $R$,they experience a force $F_2$. The ratio of $F_1$ to $F_2$ is:

Two point charges $+q_{1}$ and $+q_{2}$ are placed a finite distance '$d$' apart. It is desired to put a third charge $q_{3}$ in between these two charges so that $q_{3}$ is in equilibrium. This is

Two point charges of equal magnitude but opposite sign are placed at a certain distance. The force between them is $F$. If $75\%$ of the charge from one is transferred to the other,what will be the new force between them?

$A$ particle of mass $M$ and charge $q$ is placed at the midpoint between two fixed charges each of magnitude $Q$, separated by a distance $2d$. The system is collinear as shown in the figure. If the particle is displaced by a small distance $x$ $(x \ll d)$ along the line joining the two charges and released, it will oscillate about the mean position with a time period $T$. ($\varepsilon_{0}$ is the permittivity of free space)

Two small spherical balls each carrying a charge $Q = 10\,\mu C$ are suspended by two insulating threads of equal lengths $L = 3\, m$ each,from a point fixed in the ceiling. It is found that in equilibrium,the threads are separated by an angle of $120^{\circ}$ between them,as shown in the figure. What is the tension in the threads? (Given: $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\, N\cdot m^2/C^2$)

$A$ charge $Q$ is divided into two parts $Q_1$ and $Q_2$. These charges are placed at a distance $R$. What will be the values of $Q_1$ and $Q_2$ for the maximum repulsive force between them?