Two charges of $+2\,C$ and $+6\,C$ repel each other with a force of $12\,N$. If each charge is given an additional charge of $-2\,C$,what will be the new force between them?

Two identical spheres each of radius $R$ are kept at a center-to-center spacing of $4R$ as shown in the figure. They are charged,and the electrostatic force of interaction between them is first calculated assuming them to be point-like charges at their centers $(F_c)$,and the force is also measured experimentally $(F_m)$. ($F_c$ and $F_m$ denote the magnitude of the force.)

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting,massless strings of same length. At equilibrium,the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $\rho_l = 800 \ kg \ m^{-3}$ and dielectric constant $K = 21$. If the angle between the strings remains the same after the immersion,then
$(A)$ electric force between the spheres remains unchanged
$(B)$ electric force between the spheres reduces
$(C)$ mass density of the spheres is $840 \ kg \ m^{-3}$
$(D)$ the tension in the strings holding the spheres remains unchanged

When air is replaced by a dielectric medium of constant $k$,the maximum force of attraction between two charges separated by a distance $r$:

Two pith balls carrying equal charges are suspended from a common point by strings of equal length. The equilibrium separation between them is $r$. Now,the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:

The magnitude of the electric force on a $2\, \mu C$ charge placed at the centre $O$ of two equilateral triangles,each of side $10\, cm$,as shown in the figure,is $P$. If the charges at $A, B, C, D, E,$ and $F$ are $2\, \mu C, 2\, \mu C, 2\, \mu C, -2\, \mu C, -2\, \mu C,$ and $-2\, \mu C$ respectively,then $P$ is: ..... $N$