Give reason : ''Small and light pieces of paper are attracted by comb run through dry hair.''

Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero

Two point charge $-q$ and $+q/2$ are situated at the origin and at the point $(a, 0, 0)$ respectively. The point along the $X$ - axis where the electric field vanishes is

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 ?

A charged oil drop is suspended in a uniform field of $3 \times$ $10^{4} V / m$ so that it neither falls nor rises. The charge on the drop will be $.....\times 10^{-18}\; C$

(take the mass of the charge $=9.9 \times 10^{-15} kg$ and $g=10 m / s ^{2}$ )

A uniformly charged disc of radius $R$ having surface charge density $\sigma$ is placed in the ${xy}$ plane with its center at the origin. Find the electric field intensity along the $z$-axis at a distance $Z$ from origin :-