Electric potential is the electric potential energy per unit charge. We know the potential energy of test charge \(q_0\) and point charge \(q\) and therefore the electric potential is
\[V = \frac{{\left( {k\frac{{q{q_0}}}{r}} \right)}}{{{q_0}}} = k\frac{q}{r} \tag{1}\]
The above equation shows that the electric potential is independent of \(q_0\). The SI unit of electric potential or simply potential is J/C or volt written as V.
Now the electric potential due to the collection of charges \(q_1\), \(q_2\), \(q_3\), \(q_4\) etc. at a point say \(p\) at distance \(r_1\), \(r_2\), \(r_3\) and \(r_4\) respectively is the sum of the potentials due to individual charges.
\[\begin{align*} {V_{{\rm{total}}}} &= k\left( {\frac{{{q_1}}}{{{r_1}}} + \frac{{{q_2}}}{{{r_2}}} + \frac{{{q_3}}}{{{r_3}}} + \frac{{{q_4}}}{{{r_4}}}} \right)\\ {\rm{or,}}\quad {V_{{\rm{total}}}} &= k\sum\limits_{n = 1}^n {\frac{{{q_n}}}{{{r_n}}}} \tag{2} \end{align*}\]
If the electric charge is uniformly distributed over a surface or throughout a volume, we can make a small element of charge \(dq\) and determine the electric potential at any point inside the electric field. The total electric potential due to the surface or volume of charge is the sum of electric potentials due to all element charges.
\[V = k\int {\frac{{dq}}{r}} \tag{3}\]
