The value of the electric permittivity of free space $(\varepsilon_0)$ is ........

Charges $q, 2q, 3q,$ and $4q$ are placed at the corners of a square as shown in the figure. $A$ charge $q_0$ is placed at its center. Find the net force on the charge $q_0$.

Two identical charges are separated by a distance $d$. $A$ third charge is placed on their perpendicular bisector at a distance $x$. For the third charge to experience maximum force,the value of $x$ is:

Charges $3Q$,$q$,and $Q$ are placed along the $x$-axis at positions $x=0$,$x=l/3$,and $x=l$ respectively. When the net force on charge $Q$ is zero,the value of $q$ is:

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 $\theta_{1}=\theta_{2}$?

The electrostatic force of interaction between a uniformly charged rod having total charge $Q$ and length $L$ and a point charge $q$ as shown in the figure is: