Derive an expression for the intensity due to a point charge

Intensity of Electric field : It is defined as the force experienced per unit positive test charge placed at that point in the field $\mathrm{E}=\frac{\mathrm{F}}{\mathrm{Q}}$
Intensity if electric field due to point charge:
Consider a positive charge is placed at point A. Imagine a test charge Q₀ at point P . Which is at a distance 'd' from point 'A'. The force on test charge is
$\mathrm{F}=\frac{1}{4{\mathrm{\pi ϵ}}_0}\frac{{\mathrm{QQ}}_0}{{\mathrm{d}}^2}$

Intensity of electric field at point P is $\mathrm{E}=\frac{\mathrm{F}}{{\mathrm{Q}}_0}$
$\mathrm{E}=\frac{1}{4\mathrm{\pi }{\in }_0}\frac{\mathrm{Q}}{{\mathrm{d}}^2}$ is along the force experienced by the test charge Q₀