In nature there are four different types of forces. The gravitational forces, the electromagnetic forces, the nuclear strong and nuclear weak forces. The first two type of forces are long range forces, in what it concern the distance over they are effective. In the following will will refer only to gravitational force, the study of electromagnetic forces being the same.
As we know the gravitational force can be written as
`F = G*(m*M)/R^2` and we can associate a force field to it
`E = GM/R^2`
(the force field is equal to the force that acts on the unity mass `m=1` kg).
Now, every force field can do work on an exterior body. The work of the gravitational force is just
`W =int_0^(+oo) F*dR =-G(mM)/R =-m*(GM/R) =-m*U` (1)
Experimentally it has been found that the work of the gravitational field doe not depend on the path taken. (The value of the integral above does not depend on the path between starting point `R=0` and last point `R=+oo` ). This means that the filed is conservative. In these conditions one can define a potential `U` of the field `E` (see the above relation) such that
`E= -grad U` (2)
Therefore a potential is defined for a conservative field using the above relation(2). As can be seen from (1) a high potential means that the field can do work on a mass moving it to a lower potential.