How is the minimum reasonable distance for the far field of a dipole antenna calculated?

Question

First let me try to explain what I think the near field is about:

At very close ranges, due to the differences between instantanous voltage and current on each small segment of an antenna at any given time, the EM field is not uniform (spherically) yet. If the antennas (reciever and transmitter) are this close, the mutual inductions are lame and reactive. Induced currents at various segments of the recieving antenna could contradict and impede each other.

But I can't be certain about how the minimum distance (to avoid these negative effects) is calculated?

Some sources say the distance should be more than 2 wavelengths. Others say 10 wavelengths. Some calculate it as 50(L^2)/λ (L:antenna length) or 5λ/2π or λ/2π or 2(L^2)/λ. They all seem to be based on different ways of understanding/analysing.

Is there a safe method/equation commonly used in practice to calculate this minimum distance?

Edit due to comments:

You describe the near field as lame and reactive but they will still produce a decent signal in a receiving antenna so please explain your doubt or what the real problem is.

I have no references for this but if the EM waves have a finite and constant velocity, then the EM fields expanding from each segment of the antenna should be ariving at the other segments of the other antenna with a delay high enough to cause contradicting currents.

The "contradiction" should be more if,

1- The change rates of current and voltage over the antenna length from segment to segment is higher. It's hard to explain for me. If all segments of the antenna was introduced to a EM plane wave, all electrons would be forced to move at the same time, blocking or impeding each others movement/momentum less (like the situation in Betz limit or Carnot limit as a rough analogy. You try to push air with air and some of the momentum you give is turned into heat which I could define as "a sum of chaotic momentums with zero net momentum vector in total").

However, when the rate of change in magnetic and electric fields are more different on each segment of the recieving antenna, there should be disorder, concentration and rarefication of electrons at the same instant thus causing joule heating, impedance and "turbulant micro-currents" so to say. The efficiency of power transmission would be "lame".

All these simply mean that the wavelength of AC would be smaller relative to the antenna length (assuming the electrical signal velocity and AC amplitude is kept constant).

2- The distance between the antenna becomes smaller relative to the antenna length so that there would be longer time lags (phase delays) between various segments of each antenna. It's also not easy to describe. I

These are just my reasonings based mostly on studies on credible sources but don't anybody take them as scientific knowledge.

First you would need to define what you mean by "safe" or "reasonable" and that will be in terms of, what error can you accept, or what deviation from the far field model is acceptable in your specific application?

To clarify this I have little choice but to introduce the main problem I've been struggling to solve which is on the Physics Stack Exchange section. I don't know if this is against the forum rules so apologies in advance. I don't mean to ask the same question here of course:

https://physics.stackexchange.com/questions/293097/average-force-between-two-parallel-finite-wires-with-ac

Please check out the last comment made by Void. According to this comment, what I mean by "safe" is the distance that the electric and magnetic fields expanding from the antenna start behaving like a regular EM wave.

Interest only: The near field of the Jodrell Bank Radio Telescope - also used for deep space communications, extends to beyond the atmosphere. This tends to make pre-flight integrated system testing "hard" :-).

Wouldn't this like measuring the minute changes in the stray/parasitic inductances of a huge transformer? Just a wild guess.

Sorry for the lengthy edit. Maybe because I have too few friends around to talk about science.

Answer 1

An antenna produces fields that fall into three categories: -

And, the generally accepted formulas for these are: -

So, if the largest dimension were 0.75 metres and the frequency was 100 MHz (i.e. a quarter wave monopole), the reactive near field is done at 24 cm and the far field begins at about 38 cm.

However, for a dish with diameter 7.5 metres (at 100 MHz), the reactive near field extends to about 7.4 metres and the far field begins at about 37.5 metres.

This site has a calculator and is where I took the formulas from. The formulas are generally accepted as being meaningful but, there are no hard and fast rules or limits.

This site also uses the same formulas and has a nice picture that shows how the fields gradually converge in amplitude to produce a proper EM wave at an impedance of 377 ohms (free space impedance). This is for an electrically "short" antenna: -

Wiki(Near and far field) also uses the same system for calculating the near and far fields: -

Answer 2

An antenna launches a complicated field that can be split conceptually into two parts

a) a non-propagating near field, that falls off as distance cubed, which is either predominantly electric with an impedance above that of free space, or magnetic with an impedance below free space

b) a propagating far field, that falls of as distance squared, an electromagnetic wave with an impedance of free space

A threshhold distance where one or the other dominates cannot be established without specifying the ratio of the two intensities, so the distance at which they're equal, or 10% far field left, or 1%?

In practice, most workers take 2 lengths, twice the larger of the wavelength or the antenna length, as the limit of the influence of the near field. But define 'influence' in your own way, and you'll have your own threshhold distance.