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

(N/A) Definition of Electric Field: The region surrounding an electric charge in which its influence can be experienced by another charge is called the electric field of that charge.
Electric Field due to a Point Charge:
Suppose a point charge $Q$ is placed at the origin $O$ in free space. If a test charge $q$ is placed at a distance $r$ at point $P$ (where $OP = r$),then according to Coulomb's law,the force acting on $q$ is:
$\overrightarrow{F} = \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q q}{r^{2}} \hat{r}$
The electric field $\overrightarrow{E}$ at a point is defined as the force experienced by a unit positive test charge placed at that point:
$\overrightarrow{E} = \frac{\overrightarrow{F}}{q}$
Substituting the expression for force:
$\overrightarrow{E} = \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q}{r^{2}} \hat{r}$ or $E = \frac{k Q}{r^{2}}$
Key Properties:
$1$. Electric field $\overrightarrow{E}$ is also known as electric field intensity.
$2$. The force acting on a charge $q$ at position vector $\vec{r}$ is given by $\overrightarrow{F}(\vec{r}) = q \overrightarrow{E}(\vec{r})$.
$3$. The $SI$ unit of electric field intensity is $N C^{-1}$ or $V m^{-1}$.
$4$. The dimensional formula is $[M^{1} L^{1} T^{-3} A^{-1}]$.