Ask a question about 'Force field (physics)'
Start a new discussion about 'Force field (physics)'
Answer questions from other users
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
a force field
is a vector field
In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...
that describes a non-contact force
A non-contact force is a force applied to an object by another body that is not in direct contact with it. The most familiar example of a non-contact force is gravity. In contrast a contact force is a force applied to a body by another body that is in contact with it...
acting on a particle at various positions in space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...
. Specifically, a force field is a vector field
is the force that a particle would feel if it were at the point
Examples of force fields
Restriction to position-dependent forces
Some forces, including friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
, air drag, and the magnetic force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
on a charged particle, depend on the particle's velocity as well as its position. Therefore these forces are not characterized by a force field.
Work done by a force field
As a particle moves through a force field along a path C
, the work done by the force is a line integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.The function to be integrated may be a scalar field or a vector field...
This value is independent of the velocity that the particle travels along the path. For a conservative force field
A conservative force is a force with the property that the work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the net work done by a conservative force is zero.It is possible to define a numerical value of...
, it is also independent of the path itself, but depends only on the starting and ending points. Therefore, if the starting and ending points are the same, the work is zero for a conservative force field.