Total posts : 45366
At first, I suspected that the boundary of the near field may be lambda/(3*pi) (not lambda/2*pi) because of the following reasons:
1. It is close to .1*lambda, which is the number I got from field graphs for short antennas. 1/3*pi = .106103295. 1/(2*pi) = .159154943.
2. Factors of the form 1/(n*pi), where n is the integer 1,2,3,4, or 6, occur frequently in antenna theory. Strictly speaking, this is not a logical reason for selecting a number from this set, but mathematics is more of an experimental science than one would expect. One starts with a conjecture, and then tests it with calculations. Then, if the conjecture appears like it may be correct, a mathematician attempts a formal proof.
When I used the factor lambda/(3*pi) for the radial distance from the short antenna in the formula for the vertical electric field of a differential current element (a differential current element is the limiting case of a short antenna), the real part of the field had a magnitude that was 8/3 of the magnitude of the imaginary part. I did not see any particular significance of this result for defining the boundary between the near field and the far field. Using the way the break points in a Bode plot are defined, I found the radial distance at which the real part of the electric field has the same magnitude as the imaginary part, which is (.0983634)*lambda. I reported this value in my previous post.
After reading about the Balanis reference, I checked the the vertical electric field if the distance from the antenna is lambda/(2*pi). The real part of the electic field is zero, and the imaginary part has a finite value.
The graphs I used are much closer to my value for the radius of the near field boundary than that of Balanis. I think that the reason for this is because the graphs are drawn in the manner of Bode plots, with straight lines drawn on a logarithmic scale. My method for determining the boundary calculates the Bode break point. The Balanis value is the radianlength, which is often used in antenna theory.
I think that both the Bode break point and the radianlength are equally valid values for the near field boundary for short antennas. The near field and the far field do not have a sharp boundary. The transition from the near field to the far field is gradual. The location of the boundary is rather arbitrary.