Four electric charges $2 \mu C, Q, 4 \mu C$ and $12 \mu C$ are placed on the $x$-axis at distances $x=0, 1 \ cm, 2 \ cm$ and $4 \ cm$ respectively. If the net force acting on the charge at the origin is zero,then $Q=$ (in $\mu C$)

$A$ particle of mass $1 \, mg$ and charge $q$ is placed at the midpoint of two stationary particles,each carrying the same charge $q$,kept at a distance of $2 \, m$. If the free charged particle is displaced from its equilibrium position by a small distance $x$ $(x \ll 1 \, m)$,it executes $SHM$. Its angular frequency of oscillation will be $.... \times 10^{8} \, rad/s$ if $q^{2} = 10 \, C^{2}$.

Two positive ions,each carrying a charge $q,$ are separated by a distance $d.$ If $F$ is the force of repulsion between the ions,the number of electrons missing from each ion will be ($e$ being the charge on an electron).

An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius $r$. The Coulomb force $\vec{F}$ between the two is

Two particles with charges $+3.72 \mu C$ and $+1.86 \mu C$ are at some distance apart. If $20 \%$ of the charge is transferred from the first particle to the second particle,then the electrostatic force between them is

Two charges $2 C$ and $6 C$ are separated by a finite distance. If a charge of $-4 C$ is added to each of them, the initial force of $12 \times 10^3 \,N$ will change to