What is the relevance of potential energy as a concept?

Question

As far as I understand, for an object to have a fixed quantity of potential energy, it must be in current equilibrium and have no net force applied to it (otherwise the potential would convert to kinetic). For example, I picture a ball on a hill as a classical example.

And as far as I know, potential energy also requires some external perturbation to convert it into kinetic energy (i.e. someone pushing the ball).

But what can be said about potential energy where two fundamental forces are pushing directly against each other? i.e. the ball has rolled to the ground, but it still has a gravitational force vector pushing it downwards, however it is balanced by an equal and opposite electromagnetic force vector. The potential is still there because the force vector exists, but it would be almost impossible to do anything useful with it because of the nature of the equilibrium.

So here is the conclusion I'm making that I'd like to check the correctness of:

Potential energy is just a measure of the force vector applied by a fundamental force on an object, and the amount of "perturbation" that one has to do to turn that energy into kinetic energy is completely arbitrary, thus some potential energy is very functional (requires only a small push to get the ball rolling) whereas other equivalent potential energy would require even more work done on the system to turn the potential into kinetic, thus rendering it "unharnessable".

Edit

I've just realized that since force fields aren't homogeneous, a force vector at a given point wouldn't adequately represent potential energy. But aside from that correction, the underlying inquiry I have still remains.

Answer 1

As the name suggests, when something has Potential Energy, it just means that it has the potential to do some work.

The amount of Potential Energy that any body possesses when associated with a force depends on the position of that body. For example, the higher you go, more is your potential to drop and do some 'work'. The work that the body does only depends on its starting and end position. It has nothing to do with the trajectory.

It does not matter if the body is in equilibrium or not. A book kept on your table is also in equilibrium, its weight and normal force cancel out each other. But, it still possesses Potential Energy because it is at a height from the floor, which is the reference frame that we have chose to have zero potential.

You can apple the same logic to any type of potential energy, gravitational, electric, spring etc.

Force fields don't have to be homogeneous. If the field does some work by moving a body from one point to another in such a way that it gains potential energy, the potential energy can be evaluated as a function between the two end points.