$4 \times 10^{10}$ electrons are removed from a neutral metal sphere of diameter $20 \text{ cm}$ placed in air. The magnitude of the electric field (in $\text{N C}^{-1}$) at a distance of $20 \text{ cm}$ from its centre is:

Explain the concept of an electric field and derive the expression for the electric field due to a point charge.

$A$ charge of $3 \ C$ experiences a force of $3000 \ N$ when placed in a uniform electric field. The potential difference between two points separated by a distance of $1 \ cm$ along the field lines is.....$V$

The magnitude of electric field intensity $E$ such that an electron placed in it would experience an electrical force equal to its weight is given by:

Five charges,each $q$,are placed at the corners of a regular pentagon of side $a$ as shown in the 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 the pentagon is replaced by an $n$-sided regular polygon with charge $q$ at each of its corners?

$A$ charged particle having some mass is resting in equilibrium at a height $H$ above the centre of a uniformly charged non-conducting horizontal ring of radius $R$. The force of gravity acts downwards. The equilibrium of the particle will be stable if: