# Work by a conservative force

**^Work by a conservative force**

Work done by a conservative force in moving a body from one point say ‘A’ to other point say ‘B’ is always equal to

loss of potential energy between same points i.e.,

Here the negative sign implies that a conservative force is always directed in the direction of decreasing

potential energy (i.e. increasing stability).Dropping the integral sign & the dot product in the LCF, we can write,

i.e. a conservative force is equal to the negative of potential energy gradient.

In vector form the above result can be expresses as

For one dimensional force we can write