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

A hollow sphere of charge does not produce an electric field at any

Two parallel large thin metal sheets have equal surface charge densities $(\sigma = 26.4 \times 10^{-12}\,c/m^2)$ of opposite signs. The electric field between these sheets is

Three charges are placed as shown in figure. The magnitude of $q_1$ is $2.00\, \mu C$, but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+4.00\, \mu C$, and the net force on $q_3$ is entirely in the negative $x-$ direction. The magnitude of $q_2$ is

An electron experiences a force equal to its weight when placed in an electric field. The intensity of the field will be

Five charges, $\mathrm{q}$ each are placed at the corners of a regular pentagon of side $\mathrm{'a'}$ as in figure.

$(a)$ $(i)$ What will be the electric field at $O$, the centre of the pentagon ?

$(ii)$ What will be the electric field at $O$ if the charge from one of the corners (say $A$ $)$ is removed ?

$(iii)$ What will be the electric field at $O $ if the charge $q$ at $A$ is replaced by$ -q$ ?

$(b) $ How would your answer to $(a)$ be affected if pentagon is replaced by $n\,-$ sided regular polygon with charge $q$ at each of its corners ?