# Field

From AMS Glossary

(Redirected from Vector field)

## field

In its restricted physical sense, any physical quantity that varies in three-dimensional space (and possibly time), usually continuously except possibly on surfaces or curves.

Field quantities often satisfy partial differential equations. An example of a scalar field is the temperature

*T*(*x*,*y*,*z*,*t*) at time*t*at each point (*x*,*y*,*z*) of a solid body; an example of a vector field is the (local) velocity field**v**(*x*,*y*,*z*,*t*) in a fluid, the separate parts of which are in motion relative to each other. The continuity of these fields is a mathematical fiction, obtained by averaging over volumes containing many atoms or molecules but still small on a macroscopic scale.