Obtain the equation of electric field at a point by system of $\mathrm{'n'}$ point charges.

As shown in figure, $q_{1}, q_{2}, \ldots, q_{n}$ charges are at $\vec{r}_{1}, \vec{r}_{2}, \ldots, \vec{r}_{n}$ from origin $\mathrm{O}$.

Electric field at $P$ of position vector $\overrightarrow{r_{\mathrm{IP}}}$,

$\overrightarrow{\mathrm{E}}_{1}=\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{1}}{r_{1 \mathrm{P}}^{2}} \hat{r}_{\mathrm{IP}}$

where $\hat{r}_{\mathrm{IP}}$ is unit vector in direction from $q_{1}$ to $\mathrm{P}$.

Electric field at $\mathrm{P}$ of position vector $\overrightarrow{r_{2 P}}$,

$\mathrm{E}_{2}=\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{2}}{r_{2 \mathrm{P}}^{2}} \hat{r}_{2 \mathrm{P}}$

Similarly electric fields by $q_{3}, q_{4}, \ldots, q_{n}$ at $\mathrm{P}$ are $\overrightarrow{\mathrm{E}}_{3}, \overrightarrow{\mathrm{E}_{4}}, \ldots, \overrightarrow{\mathrm{E}_{n}}$ can be obtained and resultant field $\overrightarrow{\mathrm{E}}$ can be obtained.

$\overrightarrow{\mathrm{E}}(\vec{r}) &=\overrightarrow{\mathrm{E}}_{1}(\vec{r})+\overrightarrow{\mathrm{E}}_{2}(\vec{r})+\ldots+\overrightarrow{\mathrm{E}}_{n}(\vec{r})$

$=\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{1}}{r_{1 \mathrm{P}}^{2}} \hat{r}_{1 \mathrm{P}}+\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{2}}{r_{2 \mathrm{P}}^{2}} \hat{r}_{2 \mathrm{P}}+\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{n}}{r_{n \mathrm{P}}^{2}} \hat{r}_{n \mathrm{P}}$

$\overrightarrow{\mathrm{E}}(\vec{r}) &=\frac{1}{4 \pi \epsilon_{0}} \sum^{n} \frac{q_{i}}{r_{i \mathrm{P}}^{2}} \hat{r}_{i \mathrm{P}} \text { where } i=1,2, \ldots, n$

$\overrightarrow{\mathrm{E}}$ is vector quantity and it varies by point to point in space and it is decided by positions of source charges.