 The line integral that defines work along curve "C" takes a special form if the force F is related to a scalar field φ(x) so that
In this case, work along the curve is given by
which can be evaluated using the gradient theorem to obtain
This shows that when forces are derivable from a scalar field, the work of those forces along a curve "C" is computed by evaluating the scalar field at the start point "A" and the end point "B" of the curve.This means the work integral does not depend on the path between "A" and "B" and is said to be independent of the path.Potential energy "U"=-φ(x) is traditionally defined as the negative of this scalar field so that work by the force field decreases potential energy, that is

In this case, the application of the del operator to the work function yields,
and the force F is said to be "derivable from a potential."