Walking in the hills

Graphic - hills

A convenient way to visualize any type of potential energy (and associated forces) is to imagine walking around a hilly landscape.

Potential energy corresponds to your height above some reference point, say, sea level. The direction of the force acting at any point is the vector that points downhill. You can see that no matter which path you take between two points, your potential energy change is given by the difference in height between your start and end point.

This analogy is of course exact for gravitational potential energy, where the potential energy is proportional to height, but is a convenient visualisation for all potential energies.