We’ve now studied many properties of the electric potential and seen how potential and field are connected, but we’ve not said much about how an electric potential is created. Simply put, an electric potential difference is created by separating positive and negative charges. Shuffling your feet on the carpet transfers electrons from the carpet to you, creating a potential difference between you and a doorknob that causes a spark and a shock as you touch it. Charging a capacitor by moving electrons from one plate to the other creates a potential difference across the capacitor.

As FIGURE 26.17 shows, moving charge from one electrode to another creates an electric field $\vec{E}$ pointing from the positive toward the negative electrode. As a consequence, there is a potential difference between the electrodes that is given by

where the integral runs from any point on the negative electrode to any point on the positive. The net charge is zero, but pulling the positive and negative charges apart creates a potential difference.

FIGURE 26.17 A charge separation creates a potential difference.

Now electric forces try to bring positive and negative charges together, so a nonelectrical process is needed to separate charges. As an example, the Van de Graaff generator shown in FIGURE 26.18a separates charges mechanically. A moving plastic or leather belt is charged, then the charge is mechanically transported via the conveyor belt to the spherical electrode at the top of the insulating column. The charging of the belt could be done by friction, but in practice a corona discharge created by the strong electric field at the tip of a needle is more efficient and reliable.

FIGURE 26.18 A Van de Graaff generator.

Full Alternative Text

A Van de Graaff generator has two noteworthy features:

• Charge is mechanically transported from the negative side to the positive side. This charge separation creates a potential difference between the spherical electrode and its surroundings.

• The electric field of the spherical electrode exerts a downward force on the positive charges moving up the belt. Consequently, work must be done to “lift” the positive charges. The work is done by the electric motor that runs the belt.

A classroom-demonstration Van de Graaff generator like the one shown in FIGURE 26.18b creates a potential difference of several hundred thousand volts between the upper sphere and its surroundings. The maximum potential is reached when the electric field near the sphere becomes large enough to cause a breakdown of the air. This produces a spark and temporarily discharges the sphere. A large Van de Graaff generator surrounded by vacuum can reach a potential of 20 MV or more. These generators are used to accelerate protons for nuclear physics experiments.