Two electric charges $4q$ and $q$ are placed at a distance $l$ apart. $A$ third charge $Q$ is placed between them at the midpoint. If the resultant force on charge $q$ is zero,then the value of $Q$ is:

$A$ 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:

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

Three point charges of magnitude $5 \mu C$,$0.16 \mu C$,and $0.3 \mu C$ are located at the vertices $A$,$B$,and $C$ of a right-angled triangle whose sides are $AB = 3 \, cm$,$BC = 3 \sqrt{2} \, cm$,and $CA = 3 \, cm$. Point $A$ is the right-angle corner. Calculate the magnitude of the net electrostatic force (in $N$) experienced by the charge at point $A$ due to the other two charges.

Force of attraction between two point charges $Q$ and $-Q$ separated by $d \, \text{m}$ is $F_e$. When these charges are placed on two identical spheres of radius $R = 0.3 \, d$ whose centres are $d \, \text{m}$ apart,the force of attraction between them is

Three charges $-q_1$,$+q_2$,and $-q_3$ are placed as shown in the figure. The $x$-component of the force on $-q_1$ is proportional to