Charge $Q$ is given a displacement $\vec{r} = a\hat{i} + b\hat{j}$ in an electric field $\vec{E} = E_1\hat{i} + E_2\hat{j}$. The work done is

An oil drop of radius $2 \, mm$ with a density $3 \, g \, cm^{-3}$ is held stationary under a constant electric field $3.55 \times 10^{5} \, V \, m^{-1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (Consider $g = 9.81 \, m \, s^{-2}$)

An electron is moving towards the $x$-axis. If an electric field is applied along the $y$-direction,what is the path of the electron?

$A$ charged particle $q$ is shot towards another charged particle $Q$ which is fixed,with a speed $v$. It approaches $Q$ up to a closest distance $r$ and then returns. If $q$ were given a speed $2v$,the closest distance of approach would be

Two identical positive charges $Q$ each are fixed at a distance of $2a$ apart from each other. Another point charge $q_0$ with mass $m$ is placed at the midpoint between the two fixed charges. For a small displacement $x$ along the line joining the fixed charges,the charge $q_0$ executes $SHM$. The time period of oscillation of charge $q_0$ will be:

$A$ particle with charge $q$ approaches a fixed particle with charge $Q$ with an initial velocity $v$. It comes to a stop at a closest distance $r$ from $Q$. If the particle $q$ is given an initial velocity $2v$,the closest distance will be: