Question

Define intensity of electric field at a point. Derive an expression for the electric field intensity due to a point charge.

Answer 1

Electric field intensity is the strength of an electric field at any point. It is equal to the electric force per unit charge experienced by a test charge placed at that point, or $E=\frac{F}{q}$

From Gauss law, considering a spherical surface with charge at its center as Gaussian surface,

$E\left(A\right)=\frac{q}{{ϵ}_0}$
$⟹E\left(4\pi r^2\right)=\frac{q}{{ϵ}_0}$

$⟹E=\frac{q}{4\pi {ϵ}_0{r}^2}$

which is the intensity of electric field at a distance $r$ from the charge.