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

$A$ charged particle of mass $m_{1}$ and charge $q_{1}$ is revolving in a circle of radius $r$. Another charged particle of charge $q_{2}$ and mass $m_{2}$ is situated at the centre of the circle. If the velocity and time period of the revolving particle are $v$ and $T$ respectively, then:

$A$ 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 identical conducting spheres carrying different charges attract each other with a force $F$ when placed in air at a distance $d$ apart. The spheres are brought into contact and then returned to their original positions. Now,the two spheres repel each other with a force whose magnitude is equal to the initial attractive force. The ratio between the initial charges on the spheres is:

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:

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