In the common crystal structure of $CsCl$,$Cs^+$ and $Cl^-$ ions are arranged in a $bcc$ structure as shown in the figure. The net electrostatic force on the $Cl^-$ ion due to the eight $Cs^+$ ions is .......

The force between two identical spheres charged with the same charge $q$ is $F$. If $50\%$ of the charge from one sphere is transferred to the second sphere,then the new force will be:

Two beads,each with charge $q$ and mass $m$,are on a horizontal,frictionless,non-conducting,circular hoop of radius $R$. One of the beads is glued to the hoop at some point,while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ $\varepsilon_0$ is the permittivity of free space.]

Electrostatic force between two identical charges placed in vacuum at a distance of $r$ is $F$. $A$ slab of width $\frac{r}{5}$ and dielectric constant $9$ is inserted between these two charges. The new force between the charges is:

$ABC$ is a right-angled triangle in which $AB = 3\,cm$ and $BC = 4\,cm$. And $\angle ABC = \pi / 2$. The three charges $+15\,e.s.u.$,$+12\,e.s.u.$,and $-20\,e.s.u.$ are placed respectively on $A$,$B$,and $C$. The force acting on $B$ is.......$dynes$.

$A$ charge $Q$ is placed at the midpoint of the line joining two identical point charges $q$. For what value of $q$ will the system be in equilibrium?