Electric potential is the potential energy per unit charge, and potential difference or voltage is the difference of the potentials at any two points in an electric field.
Potential in other words is the total push until the unit charge at a particular point in electric field reaches zero potential. Potential is not a force, the term push is not a force either, the mass times the acceleration which you may know quiet well is not a force either! Then, what is force?
The difference of two potentials is the same as work done per unit charge over the displacement in the direction of electric field. The potential difference is also called voltage and its unit is called volt denoted by \(\text{V}\).
Beware that, voltage is the difference of potentials, and don't get confused by the letter \(V\) for potential and \(\text{V}\) for the unit.
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 \(b\).
The difference \(V_a - V_b\) is called the potential difference or 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 \(V_{ab}\),
\[{V_{ab}} = k\frac{q}{{{r_a}}} - k\frac{q}{{{r_b}}} = {V_a} - {V_b}\tag{1} \label{1}\]
Batteries always come up with a particular voltage associated with them. The positive and negative charges are separated by a chemical reaction. When you connect one terminal of a battery to a load such as bulb and also connect additional resistance if required in the circuit for safety purposes, finally connect the combination of load and additional resistance to the negative terminal, the bulb will glow. The positive and negative terminals of the battery create a potential difference. The work done by the electric field per unit charge at the positive terminal of the battery to the negative terminal is the voltage.
Never connect positive terminal of a battery to the negative terminal as it causes short circuit and can cause serious accident and even death! You must know what you are doing!
