Write the equation for the electric field produced by a system of $n$ charges.

(N/A) According to the principle of superposition,the electric field at a point $P$ due to a system of $n$ point charges $q_1, q_2, ..., q_n$ located at positions $\vec{r}_1, \vec{r}_2, ..., \vec{r}_n$ is the vector sum of the individual electric fields produced by each charge.
The electric field $\vec{E}$ at a position vector $\vec{r}$ is given by:
$\vec{E}(\vec{r}) = \sum_{i=1}^{n} \frac{1}{4\pi\epsilon_0} \frac{q_i}{|\vec{r} - \vec{r}_i|^3} (\vec{r} - \vec{r}_i)$
Where:
- $\epsilon_0$ is the permittivity of free space.
- $q_i$ is the magnitude of the $i$-th charge.
- $\vec{r}_i$ is the position vector of the $i$-th charge.
- $\vec{r}$ is the position vector of the point where the field is calculated.