3.2 Electric Potential and Potential Difference
LEARNING OBJECTIVES
- Define electric potential, voltage, and potential difference
- Define the electron-volt
- Calculate electric potential and potential difference from potential energy and electric field
- Describe systems in which the electron-volt is a useful unit
- Apply conservation of energy to electric systems
Recall that earlier we defined electric field to be a quantity independent of the test charge in a given system, which would nonetheless allow us to calculate the force that would result on an arbitrary test charge. (The default assumption in the absence of other information is that the test charge is positive.) We briefly defined a field for gravity, but gravity is always attractive, whereas the electric force can be either attractive or repulsive. Therefore, although potential energy is perfectly adequate in a gravitational system, it is convenient to define a quantity that allows us to calculate the work on a charge independent of the magnitude of the charge. Calculating the work directly may be difficult, since and the direction and magnitude of can be complex for multiple charges, for odd-shaped objects, and along arbitrary paths. But we do know that because , the work, and hence , is proportional to the test charge . To have a physical quantity that is independent of test charge, we define electric potential (or simply potential, since electric is understood) to be the potential energy per unit charge:
ELECTRIC POTENTIAL
The electric potential energy per unit charge is
(3.2.1)
Since U is proportional to q, the dependence on q cancels. Thus, does not depend on . The change in potential energy is crucial, so we are concerned with the difference in potential or potential difference between two points, where
ELECTRIC POTENTIAL DIFFERENCE
The electric potential difference between points and , is defined to be the change in potential energy of a charge moved from to , 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 electric 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. It is worthwhile to emphasize the distinction between potential difference and electrical potential energy.
POTENTIAL DIFFERENCE AND ELECTRICAL POTENTIAL ENERGY
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 store