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

Two charges $q_1$ and $q_2$ are placed in vacuum at a distance $d$ and the force acting between them is $F$. If a medium of dielectric constant $4$ is introduced around them,the force now will be

$(a)$ Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \; cm$. What is the mutual force of electrostatic repulsion if the charge on each is $6.5 \times 10^{-7} \; C$? The radii of $A$ and $B$ are negligible compared to the distance of separation.
$(b)$ What is the force of repulsion if each sphere is charged double the above amount,and the distance between them is halved?

The force between two charges of $+3 \ \mu C$ and $+8 \ \mu C$ is $40 \ N$. If a charge of $-5 \ \mu C$ is added to both,what will be the new force in $N$?

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:

$A$ 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: