For the regular pentagon system shown in the figure,find the net electrostatic force on the charge $q_0$ placed at the center.

Three equal charges $q_1, q_2$ and $q_3$ are placed on the three corners of a square of side $a$. If the force between $q_1$ and $q_2$ is $F_{12}$ and that between $q_1$ and $q_3$ is $F_{13}$,then the ratio of magnitudes $\left(\frac{F_{12}}{F_{13}}\right)$ is

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

$A$ point charge $q$ is situated at a distance $d$ from one end of a thin non-conducting rod of length $L$ having a charge $Q$ (uniformly distributed along its length) as shown in the figure. Then the magnitude of the electric force between them is:

Two charges $+q$ and $-3q$ are placed on the $x$-axis separated by a distance $d$. ($-3q$ is to the right of $q$). Where should a third charge $2q$ be placed such that it will not experience any net force?

Two charges $Q$ are placed at opposite corners of a square. Two charges $q$ are placed at the other two corners. If the net electric force on $Q$ is zero,then $Q/q$ is equal to: