Let's consider a ring of total charge \(q\). The centre of the ring is ths same as the origin of our coordinate system and x-axis is perpendicular to the plane of the ring. We find the electric potential at point \(p\) at distance \(x\) from the centre of the ring on x-axis (see Figure 1). The radius of the ring is \(a\). We first divide the ring of charge into infinitesimal elements of charge \(dq\) and sum up the electric potentials due to all elements by integration.
The distance between the point \(p\) and the element of charge \(dq\) is \({\sqrt {{x^2} + {a^2}} }\). The small electric potential due to the charge \(dq\) at the point \(p\) is:
\[dV = k\frac{{dq}}{{\sqrt {{x^2} + {a^2}} }}\]
The total electric potential due to the ring of charge is
\[V = k\frac{1}{{\sqrt {{x^2} + {a^2}} }}\int {dq} = k\frac{q}{{\sqrt {{x^2} + {a^2}} }}\]
