What is a conservative force field?

A conservative force field is a field in which total energy is conserved. More formally, in a conservative field, the work done in moving between two points in the field depends only on the location of these two points and not the path taken between them. The work done in going from one point to another is equal and opposite to the work done in taking the journey in reverse.

A good way to understand the difference between conservative and non-conservative forces is to imagine a simple pendulum, on Earth (i.e. in a gravitational field) swinging back and forth. In the absence of any external forces other than gravity, the pendulum's total energy would be conserved and it would keep swinging with the same amplitude forever. All the kinetic energy it loses in rising up against gravity is gained back as it swings back down again; the work done on the return journey is equal and opposite.

However, for a real pendulum, this is not the case since it is also subject to non-conservative forces such as friction between the pendulum and its pivot. Such a force does not conserve total energy as the kinetic energy it loses due to friction when swinging one way is not gained back as it makes the return journey. Instead, it loses more kinetic energy and the friction force dissipates energy from the pendulum to its surroundings, causing the size of the swings to decrease over time.