8.7 Electric potential energy: potential difference  (Page 2/9)

Since PE is proportional to $q$ , the dependence on $q$ cancels. Thus $V$ does not depend on $q$ . The change in potential energy $\text{ΔPE}$ is crucial, and so we are concerned with the difference in potential or potential difference $\mathrm{\Delta }V$ between two points, where

The potential difference between points A and B, $V_{\text{B}}–V_{\text{A}}$ , is thus defined to be the change in potential energy of a charge $q$ moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.

The familiar term voltage is the common name for potential difference. Keep in mind that whenever a voltage is quoted, it is understood to be the potential difference between two points. For example, every battery has two terminals, and its voltage is the potential difference between them. More fundamentally, the point you choose to be zero volts is arbitrary. This is analogous to the fact that gravitational potential energy has an arbitrary zero, such as sea level or perhaps a lecture hall floor.

In summary, the relationship between potential difference (or voltage) and electrical potential energy is given by

Voltage is not the same as energy. Voltage is the energy per unit charge. Thus a motorcycle battery and a car battery can both have the same voltage (more precisely, the same potential difference between battery terminals), yet one stores much more energy than the other since $\text{ΔPE =}q\mathrm{\Delta }V$ . The car battery can move more charge than the motorcycle battery, although both are 12 V batteries.