Potential energy is energy stored in a system of forcefully interacting physical entities.
he SI unit for measuring work and energy is the joule (J).
The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine.
Potential energy is associated with forces that act on a body in a way that depends only on the body's position in space. These forces can be represented by a vector at every point in space forming what is known as a vector field of forces, or a force field.
A very important point to understand about potential energy is that it is only changes in potential energy that are physically meaningful.
What do we mean by that? Well, let’s take a ball of mass M, beloved by physics textbooks, and carry it from street level to the top of the Eiffel Tower, height h. We generally say that the ball now has a potential energy of Mhg, where g is the acceleration due to gravity. What we really mean is that the ball has gained in potential energy an amount Mhg compared to its value at street level. But what was its value at street level? Who knows?! Fortunately it doesn’t really matter.
We can decide that street level will be our reference point and that the potential energy there is zero (we could choose another number or make the top of the Eiffel Tower our reference point but that would not be so convenient).
Now if we take our ball to the top of Notre Dame cathedral, height t above street level, we say its potential energy is Mtg (we now know it is really relative potential energy but we drop the word relative) and we can compare it in a meaningful way to the potential energy when at the top of the Eiffel Tower.
One further point, changes in potential energy can be positive (+) or negative (-).
In taking the ball to the top of the Eiffel Tower it gained potential energy –positive change. If we now descend half way down the Tower, the ball will lose potential energy (it’s not so high now) and the change in potential energy will be negative.
In physical systems we do not generally use street level as a reference point.
It is convenient, but somewhat abstract, when deriving mathematical expressions for potential energy ( or the related parameter potential) to use infinity as our reference point and define the potential energy at infinity to be zero, as well as dropping the word relative.
Such a procedure is commonly seen when dealing with electrical fields and, for example, accounts for the negative values of the energy levels seen in calculations of the Bohr atomic model and the strange habit when making calculations in thermochemistry of taking things to and from infinity!