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

Four point charges $q_{A}=2\; \mu C, q_{B}=-5\; \mu C,$ $q_{C}=2\; \mu C,$ and $q_{D}=-5\;\mu C$ are located at the corners of a square $ABCD$ of side $10\; cm .$ What is the force on a charge of $1 \;\mu C$ placed at the centre of the square?

Four identical pendulums are made by attaching a small ball of mass $100 \,g$ on a $20 \,cm$ long thread and suspended from the same point. Now, each ball is given charge $Q$, so that balls move away from each other with each thread making an angle of $45^{\circ}$ from the vertical. The value of $Q$ is close to ..............$\mu C$ $\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right.$ in $SI$ units $)$

Two balls of same mass and carrying equal charge are hung from a fixed support of length $l$. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$ between the balls is proportional to

Two charges, each equal to $q$, are kept at $x = -a$ and $x = a$ on the $x-$axis. A particle of mass $m$ and charge $q_0=\frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y < < a)$ along the $y-$axis, the net force acting on the particle is proportional to

Point charges $ + 4q,\, - q$ and $ + 4q$ are kept on the $x - $axis at points $x = 0,\,x = a$ and $x = 2a$ respectively, then