# Why do we want detaching field lines in an antenna?

I have some questions about the link between the intuitive explanation for why an antenna radiates (based on this video) and the Maxwell equations.

Q1. The video starts by saying that "an inductor with AC supply does not radiate" because the field-lines are just fluctuating around the source. In the animation, the field lines expand and contract around the source without detaching from it.

I don't understand this statement. Formally, I don't see any difference between Maxwell Equations for an antenna and an inductor with same AC supply. In both cases, If I take a point in space, I believe the homogeneous helmholtz equations are valid. The Ampere and Faraday Equations are identical. The only difference I can see is on the physical length of the circuit compared to the wavelength. I'd say that an inductor utilized for non-radiating purposes, the field-lines will detach much far away compared to one utilized for radiating purposes. Am I wrong?

Q2. Now it considers a dipole with AC supply. At time 0, charges start with maximum separation, zero speed and maximum acceleration. All the past time is supposed to be static so their electric field lines are the same as those of a regular static dipole.

At time 1/8 of period T, the charges have less separation, more speed, less acceleration. The field lines are not exactly the same as a static dipole or even a constant-speed dipole with same charge separation because of the retardation of field propagation (I can see this by looking at Jefimenko's Equations).

At time 1/4 of period T, the charges have zero separation, maximum speed, zero acceleration. The video says that field-lines detach from the source at this time.

Let's formalize better this last event. I'd say that zero separation between charges means there is no net charge in that volume of space. That means that the divergence of electric field (homogeneous medium) must be zero. This means that the past diverging lines cannot exist any more, so these pre-existing lines must detach from the source.

Am I wrong?

Q3. From this video it appears that for an antenna is crucial that the electric field lines detach from the source. I really don't understand this. This animation from MIT shows no detaching of field lines in a dipole because we are too close to see the detaching. But there still is a time-varying electromagnetic field in these points of space. Why do we want the field lines detach?

• The energy supplied to the antenna by a sinusoidal source is complex. The reactive component is confined to the surroundings of the antenna. The active power, however, is radiated into space theoretically up to infinity. For me this also applies to a high frequency coil. Commented Feb 10 at 11:30
• This topic is not well explained in resources - you can't look for radiation fields in Coulomb fields. These are seperate fields that arise, in one way of looking at it, to ensure continuity of field lines. Appendix H in Purcell and Morin 3rd edition explains this beautifully. Another way is to get the same result through the magnetic vector potential, but that's less intuitive. The inductor does produce radiation fields because whenever charge accelerates changes its path even at a constant speed, radiation field result to fill the discontinuity in the angle of the field lines. Commented Feb 11 at 1:32
• But very importantly- radiation fields are not to be found in Columb fields. It's even unfortunate to draw the two together in this way, like in the video, because it given the impression that radiation is Columb fields that get detached. Rather radiation fields are seperate from Columb fields, and propagate by induction. The only way they relate to Cplumb fields is that discontinuity of Coulomb fields due to acceleration of charge results in de-novo radiation fields to fill the angle discontinuity. Commented Feb 11 at 1:35

The video you have watched is taking poor analogies and 'lies to children' beyond the limits of usefulness. You would be better to un-watch it, and start again with more coherent presentations.

The first diagram you post does not show an 'inductor'. An ideal inductor has zero size, all the field is contained within its boundaries, and it does not radiate. What it shows is a magnetic dipole, a small loop antenna. It radiates. Because it is small, it radiates the far field, an electromagnetic wave that falls as $$\\frac{1}{R^2}\$$, inefficiently, but it does radiate. The most noticeable feature of a small loop antenna is the near field, which does not radiate, is predominantly magnetic, and falls as $$\\frac{1}{R^3}\$$. This is the basis of the NFC (Near Field Communication) devices we all have now. The corresponding small electric antenna is a tiny little dipole.

'Field Lines' are a fiction. They are just lines drawn on diagrams to help you visualise the field. They have no physical significance, and do not 'detach' to enable RF to propagate. While charge separation is a reasonable concept to handle, speeds and accelerations of charges are not helping anyone.

As an antenna gets larger, to the order of the wavelength, it becomes more efficient at radiating the far field. That is the only difference between small and large antennae.

If you want to think about radiation efficiency, and the difference between near and far fields, then a reasonable route in is via the impedance. The impedance of free space is 377 Ω, that's the ratio of electric to magnetic field of a propagating electromagnetic wave. The antenna is in some senses (here's my analogy which may or may not suit everybody) a transformer, that matches the impedance of free space to the electrical impedance of the feeder, which is usually 50 or 75 Ω. The impedance of a near field wave is either very low, in the magnetic NFC case, or very high, in the electric field case. Small antennae do not make good transformers.

• "An inductor has zero size, all the field is contained within its boundaries, and it does not radiate." -- perhaps in circuit theory, but not a real one. Were you quoting that video? Commented Feb 10 at 11:53

an inductor with AC supply does not radiate

That's news to anyone actually using inductors. They radiate just fine. They are not necessarily the most efficient radiators, but in most uses of inductors - in power conversion these days - you do not want them to radiate at all.

Ideal solenoids and other instructional aids are rather hard to come by in real life. The actual parts are quite far away from those ideals in many respects.

Q2

What is the blue line? How helpful is it to have just one of them?