Two equal charges $q$ are placed at $x = -a$ and $x = a$ on the $x$-axis. $A$ particle of mass $m$ and charge $q_0 = q/2$ is placed at the origin. If the charge $q_0$ is given a small displacement $(y << a)$ along the $y$-axis,the net force acting on the particle is proportional to .......

Two pith balls, each carrying charge $+q$, are hung from a hook by two strings of length $L$. It is found that when each charge is tripled, the angle between the strings doubles. What was the initial angle between the strings (in $^{\circ}$)?

Two positive charges of $20 \, C$ and $Q \, C$ are situated at a distance of $60 \, cm$. The neutral point between them is at a distance of $20 \, cm$ from the $20 \, C$ charge. The value of charge $Q$ is: (in $, C$)

Write some important points for the vector form of Coulomb's law.

Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \; cm$. The charge on each is $6.5 \times 10^{-7} \; C$. Suppose the spheres $A$ and $B$ have identical sizes. $A$ third sphere of the same size but uncharged is brought in contact with the first,then brought in contact with the second,and finally removed from both. What is the new force of repulsion between $A$ and $B$?

An infinite number of point charges,each carrying $1 \,\mu C$ charge,are placed along the y-axis at $y=1 \,m, 2 \,m, 4 \,m, 8 \,m, \ldots$. The total force on a $1 \,C$ point charge,placed at the origin,is $x \times 10^{3} \,N$. The value of $x$,to the nearest integer,is .........
[Take $\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,N m^{2}/C^{2}$]