Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be.

A particle of mass $1 \,{mg}$ and charge $q$ is lying at the mid-point of two stationary particles kept at a distance $'2 \,{m}^{\prime}$ when each is carrying same charge $'q'.$ If the free charged particle is displaced from its equilibrium position through distance $'x'$ $(x\,< \,1\, {m})$. The particle executes $SHM.$ Its angular frequency of oscillation will be $….\,\times 10^{8}\, {rad} / {s}$ if ${q}^{2}=10\, {C}^{2}$

Two small spheres each of mass $10 \,mg$ are suspended from a point by threads $0.5 \,m$ long. They are equally charged and repel each other to a distance of $0.20 \,m$. The charge on each of the sphere is $\frac{ a }{21} \times 10^{-8} \, C$. The value of $a$ will be …… .

$\left[\right.$ Given $\left.g=10 \,ms ^{-2}\right]$

In a medium, the force of attraction between two point charges, distance $d$ apart, is $F$. What distance apart should these point charges be kept in the same medium, so that the force between them becomes $16\, F$ ?

A charged particle with charge $q$ and mass $m$ starts with an initial kinetic energy $K$ at the middle of a uniformly charged spherical region of total charge $Q$ and radius $R$ . $q$ and $Q$ have opposite signs. The spherically charged region is not free to move . The value of $K_0$ is such that the particle will just reach the boundary of the spherically charged region. How much time does it take for the particle to reach the boundary of the region.