The force between two identical spheres charged with the same charge $q$ is $F$. If $50\%$ of the charge from one sphere is transferred to the second sphere,then the new force will be:

Two charges of magnitude $5\, nC$ and $-2\, nC$ are placed at points $(2\, cm, 0, 0)$ and $(x\, cm, 0, 0)$ respectively in a region of space where there is no other external field. If the electrostatic potential energy of the system is $-0.5\,\mu J$,find the value of $x$ in $cm$.

$A$ charged metallic sphere $A$ is suspended by a nylon thread. Another charged metallic sphere $B$ held by an insulating handle is brought close to $A$ such that the distance between their centres is $10 \, cm$,as shown in Figure $(a)$. The resulting repulsion of $A$ is noted (for example,by shining a beam of light and measuring the deflection of its shadow on a screen). Spheres $A$ and $B$ are touched by uncharged spheres $C$ and $D$ respectively,as shown in Figure $(b)$. $C$ and $D$ are then removed and $B$ is brought closer to $A$ to a distance of $5.0 \, cm$ between their centres,as shown in Figure $(c)$. What is the expected repulsion of $A$ on the basis of Coulomb's law? Spheres $A$ and $C$ and spheres $B$ and $D$ have identical sizes. Ignore the sizes of $A$ and $B$ in comparison to the separation between their centres.

Two identical spheres,each carrying a charge $Q = 10 \ \mu C$,are suspended from a single rigid support by strings of length $L = 1 \ m$. In the equilibrium position,if the angle between the two strings is $60^\circ$,what is the tension $T$ in the strings (in $N$)? (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9 \ N \cdot m^2/C^2$)

Assertion : The Coulomb force is the dominating force in the universe.
Reason : The Coulomb force is weaker than the gravitational force.

Two small spheres of masses $M_{1}$ and $M_{2}$ are suspended by weightless insulating threads of lengths $L_{1}$ and $L_{2}$. The spheres carry charges $Q_{1}$ and $Q_{2}$ respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of $\theta_{1}$ and $\theta_{2}$ as shown. Which one of the following conditions is essential,if $\theta_{1}=\theta_{2}$?