Three charges are placed as shown in the figure. The magnitude of $q_1$ is $2.00\, \mu C$,but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+4.00\, \mu C$,and the net force on $q_3$ is entirely in the negative $x-$ direction. The magnitude of $q_2$ is

Two free positive charges $4q$ and $q$ are at a distance $l$ apart. What charge $Q$ is needed to achieve equilibrium for the entire system and where should it be placed from charge $q$?

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: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9 \ N \cdot m^2/C^2$)

$A$ 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 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:

The distance between charges $5 \times 10^{-11} \, C$ and $-2.7 \times 10^{-11} \, C$ is $0.2 \, m$. The distance at which a third charge should be placed in order that it will not experience any force along the line joining the two charges is . . . . . . $m$.