Obtain the equation of electric field at a point due to a system of $n$ point charges.

(N/A) According to the principle of superposition,the electric field at a point due to a system of charges is the vector sum of the electric fields produced by each individual charge at that point.
Let there be $n$ point charges $q_{1}, q_{2}, \ldots, q_{n}$ located at positions with position vectors $\vec{r}_{1}, \vec{r}_{2}, \ldots, \vec{r}_{n}$ relative to an origin $O$.
The electric field $\vec{E}_{1}$ at a point $P$ with position vector $\vec{r}$ due to charge $q_{1}$ is given by:
$\vec{E}_{1} = \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{1}}{r_{1P}^{2}} \hat{r}_{1P}$
where $r_{1P} = |\vec{r} - \vec{r}_{1}|$ and $\hat{r}_{1P}$ is the unit vector directed from $q_{1}$ to $P$.
Similarly,the electric field $\vec{E}_{i}$ at point $P$ due to any charge $q_{i}$ is:
$\vec{E}_{i} = \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{i}}{r_{iP}^{2}} \hat{r}_{iP}$
The total electric field $\vec{E}$ at point $P$ is the vector sum of individual fields:
$\vec{E} = \vec{E}_{1} + \vec{E}_{2} + \ldots + \vec{E}_{n} = \sum_{i=1}^{n} \vec{E}_{i}$
Substituting the expression for $\vec{E}_{i}$:
$\vec{E}(\vec{r}) = \frac{1}{4 \pi \epsilon_{0}} \sum_{i=1}^{n} \frac{q_{i}}{r_{iP}^{2}} \hat{r}_{iP}$
Here,$\vec{E}$ is a vector quantity that varies from point to point in space,determined by the positions and magnitudes of the source charges.