Two identical conducting spheres $\mathrm{P}$ and $\mathrm{S}$ with charge $Q$ on each, repel each other with a force $16 \mathrm{~N}$. A third identical uncharged conducting sphere $\mathrm{R}$ is successively brought in contact with the two spheres. The new force of repulsion between $\mathrm{P}$ and $\mathrm{S}$ is :

Three charges $+Q, q, +Q$ are placed respectively, at distance, $0, \frac d2$ and $d$ from the origin, on the $x-$ axis. If the net force experienced by $+Q$, placed at $x = 0$, is zero, then value of $q$ is

Similar charges are placed at corners of a square and a charge $q_0$ is placed at it's centre find net force on it

Two particles $X $ and $Y$, of equal mass and with unequal positive charges, are free to move and are initially far away from each other. With $Y$ at rest, $X$ begins to move towards it with initial velocity $u$. After a long time, finally

There are two charges $+1$ microcoulombs and $+5$ microcoulombs. The ratio of the forces acting on them will be

A proton is fired at an initial velocity of $150 \,m/s$ at an angle of $60^o $ above the horizontal into a uniform electric field of $2 \times 10^{-4} \,N/C$ between two charged parallel plates as shown in figure. Then the total time the particle is in motion is :-