Force
In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.
Force field (physics)
In physics a force field is a vector field that describes a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field formula_1, where formula_2 is the force that a particle would feel if it were at the point formula_3.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, if the starting and ending points are the same, the work is zero for a conservative field:
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: