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 $\left. g =9.81\, m / s ^{2}\right)$

Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at $O$ is double the electric field when only one positive charge of same magnitude is placed at $R$. Which of the following arrangements of charges is possible for $P,\,Q,\,R,\,S,\,T,\,$ and $U$ respectively

A positively charged ball hangs from a silk thread. We put a positive test charge ${q_0}$ at a point and measure $F/{q_0}$, then it can be predicted that the electric field strength $E$

An oil drop of $12$ excess electrons is held stationary under a constant electric field of $2.55 \times 10^{4}\; N\,C ^{-1}$ (Millikan's oil drop experiment). The density of the oil is $1.26 \;g \,cm ^{-3} .$ Estimate the radius of the drop. $\left(g=9.81\; m s ^{-2} ; e=1.60 \times 10^{-19}\; \,C \right)$

Deutron and $\alpha – $ particle are put $1\,\mathop A\limits^o $ apart in air. Magnitude of intensity of electric field due to deutron at $\alpha – $ particle is