Force field (physics, $\mathbf{F}(\mathbf{x},t)$)

A force field specifies a force vector as a function of position and, when necessary, time, for a specified test body. It is a vector field. A time-independent conservative vector field has $\mathbf{F}=-\nabla V$, where $V$ is the body's potential energy; its work along a path equals the decrease in $V$. Position-dependent forces can have nonzero curl, so a scalar potential need not exist.