Explain the superposition principle for static electric forces and write its general equation.

(N/A) The principle of superposition states that when multiple point charges are present,the total electrostatic force on a given charge is the vector sum of the individual forces exerted on it by all other charges. The force between any two charges is not affected by the presence of other charges.
Consider a system of $n$ point charges $q_1, q_2, ..., q_n$ with position vectors $\vec{r}_1, \vec{r}_2, ..., \vec{r}_n$ relative to an origin $O$.
The force on charge $q_1$ due to charge $q_2$ is given by:
$\vec{F}_{12} = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{21}^2} \hat{r}_{21}$
Similarly,the force on $q_1$ due to charge $q_n$ is:
$\vec{F}_{1n} = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_n}{r_{n1}^2} \hat{r}_{n1}$
According to the superposition principle,the total force $\vec{F}_1$ on charge $q_1$ is the vector sum of these individual forces:
$\vec{F}_1 = \vec{F}_{12} + \vec{F}_{13} + ... + \vec{F}_{1n} = \sum_{i=2}^{n} \vec{F}_{1i}$
Substituting the expression for each force:
$\vec{F}_1 = \frac{q_1}{4 \pi \epsilon_0} \sum_{i=2}^{n} \frac{q_i}{r_{i1}^2} \hat{r}_{i1}$
Where $\vec{r}_{i1} = \vec{r}_1 - \vec{r}_i$ is the vector pointing from charge $q_i$ to $q_1$,and $r_{i1}$ is the magnitude of this vector.