Radiation in the Near Zone of a Small Loop Antenna

The electromagnetic fields far from any antenna can be conveniently described as the sum of the radiation fields of a series of oscillating point multipoles, of which the leading term is a dipole in many cases of practical interest. The form of the fields associated with the nth multipole is independent of the details of the physical layout of the antenna (other than that the layout determines the magnitudes of the multipole moments). However, close to the antenna the electromagnetic fields include quasistatic components as well as radiation terms. A well-known argument due to Hertz [1, 2] gives the fields in the near and far zone of an ideal point dipole. In this and companion notes [3, 4] we explore examples in which analytic expression can be given for the near and far zone fields of antennas of finite dimensions. Here, the task is to describe the electromagnetic fields, and the Poynting vector, of an oscillating current loop of radius a when a λ = 2πc/ω, where c is the speed of light and ω is the angular frequency of oscillation of the current in the loop. The current is assumed to be independent of the azimuth around the loop.