Electric Potential

The electrical potential(given by the variable V usually) is just defined as the electrical potential per unit charge of a source charge. In other words, if I took a test charge of 1 C and put it in the electric field of a source charge, the electrical potential energy it would experience is the same as the electrical potential of the source.

​

This is more useful for many physicists than electrical potential energy if you want to study the electrical field of a specific charged object and don't really care about the other charged objects in that field. The idea is highlighted by the fact that electrical potential depends on relative location, not the charge of a given charge in an electric field. As defined above, the electrical potential at a point can be expressed as

The electrical potential difference V, also known as potential difference or voltage, is the external work required to move a charge in an electrical field between 2 points. In other words, it's just the change in electrical potential between two points for a given electrical charge. This can be expressed as

The units for electrical potential are volts, defined as Joules/Coulomb. You can also express potential difference through the electric field.

This makes sense since the electrical work can be defined through W = qEd. Thus, to get the change in potential, you just divide by the charge q. This also means the units of the electric field can be expressed as volts/meter. Just like electrical potential energy, the electrical potential is a scalar so you don't divide it into vectors to find the potential. If you were to get two charges that don't have a straight vertical or horizontal line connecting them, you'd have to use the Pythagorean Theorem to find the true radius connecting them to get the correct value for electrical potential.