Conservative Forces
If the vector field associated to a force is conservative then the force is said to be a conservative force.
The most prominent examples of conservative forces are the force of gravity and the electric field associated to a static charge. According to Newton's law of gravitation, the gravitational force, acting on a mass, due to a mass which is a distance away, obeys the equation
where is the Gravitational Constant and is a unit vector pointing from towards . The force of gravity is conservative because, where
is the Gravitational potential energy.
For conservative forces, path independence can be interpreted to mean that the work done in going from a point to a point is independent of the path chosen, and that the work W done in going around a closed loop is zero:
The total energy of a particle moving under the influence of conservative forces is conserved, in the sense that a loss of potential energy is converted to an equal quantity of kinetic energy or vice versa.
Read more about this topic: Conservative Vector Field
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