Definitions and Properties

The concept of a conservative vector field is relatively simple. A conservative vector field $\vec{F}$ is a vector with the property that its line integral is independent of path. This means that for any path C from a point P to a point Q, the value of $\int_C \vec{F} \cdot d\vec{r}$is the same, so long as P and Q are fixed.

It can be shown that this also implies that the vector field $\vec{F}$ can be written as the gradient of some scalar function f. For this reason, conservative vector fields are often called gradient vector fields.