potential
Potential
Potential is the same as potential energy just per-quantity; For instance, electric potential is the electric potential energy per Coulomb (commonly known as a Volt) and gravitational potential is the gravitational potential energy per kilogram.
It represents the difference in energy between two states. In other words, how much energy you would have to put in or how much energy you would get out by going from one state to the other. This can be seen in the definition of voltage, which is a form of potential: Voltage corresponds to the work needed per unit of charge to move a positive test charge from the first point to the second point.
Difference between potential and potential energy
We'll use gravitational potential energy as an example.
Consider a rock of mass \[m\] at an elevated position, e.g. on top of a hill. The work that would have been done in lifting this mass to the elevated position would be \[mgh\], where \[h\] is the height above where the rock once was (perhaps it was originally at the foot of the hill). Now, the rock, being on top of the hill possesses a property called potential energy, which by definition is equal to \[mgh\].
If we were to take the mass out of the equation, we would be left with \[gh\]. At first glance this just represents the potential energy possessed by some body of mass 1 kilogram. However, it is more useful to think of it as a property that would be possessed by some body of unit mass if it were to be placed there. This implies that regardless of whether anything has been placed there, the potential at this point remains \[gh\].
A map can thus be made of every point on that hill with a tag indicating the potential at every point. This map is commonly known as a potential field. This is a seemingly trivial shift, but we've turned our focus from objects to points in space, which allows us to calculate problems much easier, e.g. when we want to compare potentials at different points.