According to the superposition principle}, the net force acting on a given point charge due to a number of point charges around it is the vector sum of the individual forces acting on that point charge due to all other point charges.
Consider number of point charges $q_1, q_2, q_3, \dots, q_n$ having position vectors $\vec{r}_1, \vec{r}_2, \vec{r}_3, \dots, \vec{r}_n$ respectively. Let $q_0$ be the test charge having position vector $\vec{r}_0$.
Let $\vec{F}_{01}, \vec{F}_{02}, \vec{F}_{03}, \dots, \vec{F}_{0n}$ be the forces acting on the given test charge $q_0$ due to $q_1, q_2, q_3, \dots, q_n$ respectively, then the net force acting on $q_0$ is given by
$\vec{F} = \vec{F}_{01} + \vec{F}_{02} + \vec{F}_{03} + \dots + \vec{F}_{0n}$
$\vec{F} = \sum_{i=1}^{n} \vec{F}_{0i} \quad \dots (i)$
The force acting on $q_0$ due to $q_1$ is given by
$\vec{F}_{01} = \frac{1}{4\pi\epsilon_0} \frac{q_0 q_1 (\vec{r}_0 - \vec{r}_1)}{|\vec{r}_0 - \vec{r}_1|^3} \quad \dots (ii)$
The force acting on $q_0$ due to $q_2$ is given by
$\vec{F}_{02} = \frac{1}{4\pi\epsilon_0} \frac{q_0 q_2 (\vec{r}_0 - \vec{r}_2)}{|\vec{r}_0 - \vec{r}_2|^3} \quad \dots (iii)$
The force acting on $q_0$ due to $q_3$ is given by
$\vec{F}_{03} = \frac{1}{4\pi\epsilon_0} \frac{q_0 q_3 (\vec{r}_0 - \vec{r}_3)}{|\vec{r}_0 - \vec{r}_3|^3} \quad \dots (iv)$
So on...
Substituting the values of eqns. (ii), (iii), (iv), $\dots$ in equation (i), we get,
$\vec{F}= \frac{1}{4\pi\epsilon_0} \frac{q_0 q_1 (\vec{r}_0 - \vec{r}_1)}{|\vec{r}_0 - \vec{r}_1|^3} + \frac{1}{4\pi\epsilon_0} \frac{q_0 q_2 (\vec{r}_0 - \vec{r}_2)}{|\vec{r}_0 - \vec{r}_2|^3}$
$+ \frac{1}{4\pi\epsilon_0} \frac{q_0 q_3 (\vec{r}_0 - \vec{r}_3)}{|\vec{r}_0 - \vec{r}_3|^3} + \dots + \frac{1}{4\pi\epsilon_0} \frac{q_0 q_n (\vec{r}_0 - \vec{r}_n)}{|\vec{r}_0 - \vec{r}_n|^3}$
$ \vec{F} = \frac{q_0}{4\pi\epsilon_0} \sum_{i=1}^{n} \frac{q_i (\vec{r}_0 - \vec{r}_i)}{|\vec{r}_0 - \vec{r}_i|^3}$
Importance of the Principle of Superposition:By using the principle of superposition, we can apply Coulomb's law to find the net force on a test charge due to a group of point charges around it.