Point charge $q$ moves from point $P$ to point $S$ along the path $PQRS$ (figure shown) in a uniform electric field $E$ pointing coparallel to the positive direction of the $X – $axis. The coordinates of the points $P,\,Q,\,R$ and $S$ are $(a,\,b,\,0),\;(2a,\,0,\,0),\;(a,\, – b,\,0)$ and $(0,\,0,\,0)$ respectively. The work done by the field in the above process is given by the expression

The electrostatic force on a small sphere of charge $0.4 \;\mu\, C$ due to another small sphere of charge $-0.8 \;\mu \,C$ in air is $0.2\; N .$

$(a)$ What is the distance between the two spheres?

$(b)$ What is the force on the second sphere due to the first?

${F_g}$ and ${F_e}$ represents gravitational and electrostatic force respectively between electrons situated at a distance $10\, cm$. The ratio of ${F_g}/{F_e}$ is of the order of

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 equal negative charge $-q$ are fixed at the fixed points $(0,\,a)$ and $(0,\, – a)$ on the $Y$-axis. A positive charge $Q$ is released from rest at the point $(2a,\,0)$ on the $X$-axis. The charge $Q$ will