Electric charges of $1\,\mu C,\, - 1\,\mu C$ and $2\,\mu C$ are placed in air at the corners $A$, $B$ and $C$ respectively of an equilateral triangle $ABC$ having length of each side $10 \,cm$. The resultant force on the charge at $C$ is......$N$

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 ${q}^{2}=10\, {C}^{2}$

Force between two identical spheres charged with same charge is $F$. If $50\%$ charge of one sphere is transferred to second sphere then new force will be

A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to

A $10\,\mu C$ charge is divided into two parts and placed at $1\,cm$ distance so that the repulsive force between them is maximum. The charges of the two parts are :

Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is