$(a)$ 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?

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 charges each of $1\;coulomb$ are at a distance $1\,km$ apart, the force between them is

Two fixed charges $4\,Q$ (positive) and $Q$ (negative) are located at $A$ and $B$, the distance $AB$ being $3$ $m$.

Two identical conducting spheres having unequal positive charges $q_1$ and $q_2$ separated by distance $r$. If they are made to touch each other and then separated again to the same distance, the electrostatic force between them in this case will be :-