Derive an expression for the electric potential at a point due to a system of $N$ charges.

(N/A) Consider a system of charges $q_{1}, q_{2}, q_{3}, \ldots, q_{N}$ located at distances $r_{1P}, r_{2P}, r_{3P}, \ldots, r_{NP}$ from a point $P$.
The electric potential at point $P$ due to a single charge $q_{i}$ is given by $V_{i} = \frac{1}{4 \pi \epsilon_{0}} \frac{q_{i}}{r_{iP}}$.
Since electric potential is a scalar quantity,the total electric potential $V$ at point $P$ due to the system of $N$ charges is the algebraic sum of the potentials due to individual charges:
$V = V_{1} + V_{2} + V_{3} + \ldots + V_{N}$
Substituting the expression for each potential:
$V = \frac{1}{4 \pi \epsilon_{0}} \frac{q_{1}}{r_{1P}} + \frac{1}{4 \pi \epsilon_{0}} \frac{q_{2}}{r_{2P}} + \ldots + \frac{1}{4 \pi \epsilon_{0}} \frac{q_{N}}{r_{NP}}$
Taking the common factor $\frac{1}{4 \pi \epsilon_{0}}$ out:
$V = \frac{1}{4 \pi \epsilon_{0}} \sum_{i=1}^{N} \frac{q_{i}}{r_{iP}}$
Here,$\epsilon_{0}$ is the permittivity of free space and $r_{iP}$ is the distance of the $i$-th charge from point $P$.