$A$ charge $Q$ is divided into two parts $Q_1$ and $Q_2$. For a given distance $R$,the force between them is maximum when:

$A$ 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.

Three charges $q$,$Q$,and $4q$ are placed in a straight line of length $l$ at points distant $0$,$\frac{l}{2}$,and $l$ respectively from one end. In order to make the net force on $q$ zero,the charge $Q$ must be equal to

$A$ charge of $4\,\mu C$ is to be divided into two parts. The distance between the two divided charges is constant. What should be the magnitude of the divided charges so that the electrostatic force between them is maximum?

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

$A$ point charge $q_1$ exerts a force $F$ on a point charge $q_2$. If a third charge $q_3$ is brought near the charge $q_2$,then the force exerted by $q_1$ on $q_2$ will be: