24.4: Electric Potential and Potential Difference
Suppose a positive test charge moves away from a positive static charge, then the Coulomb force does positive work, and its electric potential energy decreases. The potential energy per unit charge is defined as the electric potential. The electric potential is independent of the test charge.
When a test charge moves from the initial to the final position, the electric potential difference between those positions is defined as the ratio of the change in the potential energy to the charge on the test charge. The units of potential difference are joules per coulomb, also known as volts (V), named after Alessandro Volta. The potential difference is also called voltage, a widely used nomenclature in electronic circuits. For example, every battery has two terminals, and its voltage is the potential difference between them.
Voltage is not the same as energy. Voltage is the energy per unit charge. Thus, a motorcycle and a car battery can have the same voltage (more precisely, the same potential difference between the battery terminals), yet one stores much more energy than the other. The car battery can move more charge than the motorcycle battery, although both are 12 volt batteries.
The electric potential due to a single charge can be easily generalized to the system of multiple charges by taking the algebraic sum of the electric potential energies due to multiple charges and dividing it by the charge on the test charge. For continuous charge distribution, the potential can be calculated by integrating the charge element over the distance at which the test charge is situated.