a concept in field theory. A vector field a(P) is called a central field if there exists a point O such that all the vectors a(P) lie on straight lines passing through O and their lengths depend only on the distance r from the point P to O —that is, a(P) = f(r)n, where n is the unit vector of the line. A scalar field u(P) is said to be a central field if there exists a point O such that u(P) depends only on the distance r from the point P to O—that is, u(P) = ϕ(r).
Examples of a central vector field are the force field generated by a point charge and the gravitational force field due to a material particle. An example of a central scalar field is the field of the temperature distribution in an isotropic homogeneous body due to a point source of heat.