Three charges $-q_1$,$+q_2$,and $-q_3$ are placed as shown in the figure. The $x$-component of the force on $-q_1$ is proportional to

$A$ proton and an anti-proton come close to each other in vacuum such that the distance between them is $10 \, cm$. Consider the potential energy to be zero at infinity. The velocity at this distance will be ........... $\, m/s$.

Two identical simple pendulums each of length $L = 5 \, cm$ are suspended from the same support. When the bobs are given an equal charge of $q = 2 \, \mu C$ each, the distance between the bobs becomes $d = 6 \, cm$. Find the mass $m$ of each bob. (Take $g = 10 \, m/s^2$ and $k = 9 \times 10^9 \, N \cdot m^2/C^2$). (in $ \, kg$)

Two point charges $A$ and $B$,having charges $+Q$ and $-Q$ respectively,are placed at a certain distance apart and the force acting between them is $F$. If $25 \%$ of the charge of $A$ is transferred to $B$,then the force between the charges becomes

Two charges each of charge $+10 \mu C$ are kept on $Y$-axis at $y=-a$ and $y=+a$, respectively. Another point charge $-20 \mu C$ is placed at the origin and given a small displacement $x$ $(x \ll a)$ along $X$-axis. The force acting on the point charge is ($x$ and $a$ are in metres, $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$)

The magnitude of the electric force on a $2\, \mu C$ charge placed at the centre $O$ of two equilateral triangles,each of side $10\, cm$,as shown in the figure,is $P$. If the charges at $A, B, C, D, E,$ and $F$ are $2\, \mu C, 2\, \mu C, 2\, \mu C, -2\, \mu C, -2\, \mu C,$ and $-2\, \mu C$ respectively,then $P$ is: ..... $N$