Cylindrical Field

a concept of field theory. A vector field a(P) is said to be a cylindrical field if there exists a line, called the axis of the field, such that (1) all vectors a(P) lie on lines that pass through and are perpendicular to the axis and (2) the lengths of the vectors depend solely on the distance r of the point P to the axis, that is, a(p) = f(r)r⁰, where r⁰ is the unit vector of the line. A scalar field u(P) is said to be a cylindrical field if there exists a line, called the axis of the field, such that u(P) depends solely on the distance r of the point P to the axis, that is, u(P) = ϕ(r). An example of a vector cylindrical field is the field of electric intensity in an infinite cylindrical capacitor; an example of a scalar cylindrical field is the field of electric potential in such a capacitor.