We introduced the concept of the electric field in Chapter 22 because action at a distance raised concerns and difficulties. The field provides an intermediary through which two charges exert forces on each other. Charge $q_1$ somehow alters the space around it by creating an electric field $\vec{E}{}_1$. Charge $q_2$ then responds to the field, experiencing force $\vec{F}=q_2\vec{E}{}_1$.

In defining the electric field, we separated the charges that are the source of the field from the charge in the field. The force on charge q is related to the electric field of the source charges by

Let’s try a similar procedure for the potential energy. The electric potential energy is due to the interaction of charge q with other charges, so let’s write

FIGURE 25.15 shows this idea schematically.

FIGURE 25.15 Source charges alter the space around them by creating an electric potential.

In analogy with the electric field, we will define the electric potential V (or, for brevity, just the potential) as

Charge q is used as a probe to determine the electric potential, but the value of V is independent of q. The electric potential, like the electric field, is a property of the source charges. And, like the electric field, the electric potential fills the space around the source charges. It is there whether or not another charge is there to experience it.

In practice, we’re usually more interested in knowing the potential energy if a charge q happens to be at a point in space where the electric potential of the source charges is V. Turning Equation 25.20 around, we see that the electric potential energy is

Once the potential has been determined, it’s very easy to find the potential energy.

The unit of electric potential is the joule per coulomb, which is called the volt V:

This unit is named for Alessandro Volta, who invented the electric battery in the year 1800. Microvolts $(\mu \text{V})$, millivolts (mV), and kilovolts (kV) are commonly used units.