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

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

Two identical non-conducting thin hemispherical shells each of radius $R$ are  brought in contact to make a complete sphere . If a total charge $Q$ is uniformly distributed on them, how much minimum force $F$ will  be required to hold them together

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are $1.6 \;\mathring A$ apart is,$\left(m_{e} \simeq 9 \times 10^{-31} kg , e=1.6 \times 10^{-19} C \right)$

(Take $\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}$ )