Force field (physics)

In physics, a force field is a vector field corresponding with a non-contact force acting on a particle at various positions in space.

[1] Work is dependent on the displacement as well as the force acting on an object.

As a particle moves through a force field along a path C, the work done by the force is a line integral: This value is independent of the velocity/momentum that the particle travels along the path.

For a conservative force field, it is also independent of the path itself, depending only on the starting and ending points.

Therefore, the work for an object travelling in a closed path is zero, since its starting and ending points are the same: If the field is conservative, the work done can be more easily evaluated by realizing that a conservative vector field can be written as the gradient of some scalar potential function: The work done is then simply the difference in the value of this potential in the starting and end points of the path.