In Figure 1 the work done by the electric force from point \(a\) to point \(b\) is the potential energy at \(a\), \(U_a\) minus the potential energy at \(b\), \(U_b\).

\[{W_{{\rm{ab}}}} = {U_a} - {U_b} = \frac{{kq{q_0}}}{{{r_a}}} - \frac{{kq{q_0}}}{{{r_b}}}\]

In terms of per unit basis the work done per unit charge from point \(a\) to \(b\) is \(W_\text{ab}\) divided by \(q_0\)

\[\frac{{{W_{{\rm{ab}}}}}}{{{q_0}}} = k\frac{q}{{{r_a}}} - k\frac{q}{{{r_b}}} = {V_a} - {V_b}\]

So the work done by the electric force per unit charge from the initial position at \(a\) to the final position at \(b\) is the electric potential at \(a\) minus the electric potential at \(b\).

Figure 1 Electric potential of point \(a\) with respect to point \(b\).

The difference \(V_a - V_b\) is called the potential difference (voltage) of point \(a\) with respect to point \(b\) which is the work done but in per unit basis. If the potential of point \(a\) with respect to point \(b\) is \(V_{ab}\),

\[{V_{ab}} = k\frac{q}{{{r_a}}} - k\frac{q}{{{r_b}}} = {V_a} - {V_b}\tag{1} \label{1}\]