# Conservative force

• In conservative field, work done by the force (line integral of the force, i.e., ) is independent of the path followed between any two points.

From Fig. 6,

Fig. 6
• In conservative field, work done by the force (line integral of the force, i.e., ) over a closed path/loop is zero.

From Fig. 7,

WAâ†’B + WBâ†’A = 0

or  = 0
Fig. 7

Example

Electrostatic forces, gravitational forces, elastic forces, magnetic forces, etc., and all the central forces are conservative in nature.

# Non-conservative forces

A force is said to be non-conservative, if work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions, and for complete cycle this work done can never be a zero.

Example

Frictional force, viscous force, airdrag, etc.

Note: Work depends on frame of reference. With change of frame of reference (inertial) force does not change while displacement may change. So, the work done by a force will be different in different frames.