To understand the relationship between the force and the potential energy changes associated with that force and to be able to calculate the changes in potential energy as definite integrals. imagine that a conservative force field is defined in a certain region of space. does this sound too abstract? well, think of a gravitational field (the one that makes apples fall down and keeps the planets orbiting) or an electrostatic field existing around any electrically charged object. if a particle is moving in such a field, its change in potential energy does not depend on the particle's path and is determined only by the particle's initial and final positions. recall that, in general, the component of the net force acting on a particle equals the negative derivative of the potential energy function along the corresponding axis: