Consider a body moving from point A to B in space under an applied force. A force is conservation if the work done by the force is independent of the path followed in moving from A to B. The work however depends on the initial and the final positions; A and B only. The work in such cases in also called the line integral of the force of the field
Fig shows particle moving from A to B in three different paths 1, 2 and 3. For a conservative force.
W1 = W2 = W3
The net work done by a conservative force over any closed path is zero. Expressed mathematically.
∫F.ds = 0
Gravitational and electrostatic fields are examples of conservative fields and the corresponding forces are called conservative forces. The energy is stored in the system when work in done against conservative force.
