Relation between equivalent antenna radius and transverse line dipole moments of a narrow slot aperture having depth

A simple general relationship is shown to exist between the equivalent radius and the transverse line dipole moments of a narrow slot aperture having depth. The cross-sectional dimensions of the aperture are assumed to be small compared to both its length and the wavelength. The general relationship can be put succinctly; the perfect magnetic cylinder, having the equivalent radius of an aperture with depth, has not only the same properties but also the same transverse line dipole moments of the aperture