Dear Peter,
"Could I ask what vector potential is?" - Thank you for asking! I spent
many years asking the same question and the usual answer that I got was
that it was something to do with fluid mechanics or Maxwell's equations
(which were based on fluid mechanics). As you correctly state there is
something which is denoted by the vector A which, when it curls, produces
the magnetic field, H. Hence, mathematically it is just a mysterious
function, first recognised circa 1850, which, when it curls, produces the
magnetic field. Hence the later association of it with the term Magnetic
vector potential. It was later found that one could derive all of
Maxwel',s equations from this single equation, so it began to seem that
there was something more to it than just a pretty name. It was later
discovered (circa 1930) that the RETARDED potential emitted from an
oscillator, accelerated electron, or what you will ( i.e.the signal
emitted from a distant transmitter at any wavelength) corresponded to this
same vector potential and its polarisation in free space always remained
parallel to the distant source. The next breakthrough came circa 1960 when
Abranov and Bohm wrote a letter to Nature prophesising, on very good
grounds, that in electron interference experiments, where a beam of
electrons is fired at a double slit, it should be possible to change the
phase of the interference pattern on the screen behind the slits by
introducing a small source of vector potential, derived of its magnetic
field component, eg by using a very long thin solenoid or, in later work a
tiny toroidal coil, half way between the slits. This was later
demonstrated many times experimentally and it was clearly shown that only
the vector potential was responsible for the phenomenon, so some people,
mainly physicists at that time, began to have a real respect for it. The
engineers were much slower at recognising its importance in radio signal
emission and radiation but in the last decade it has recieved considerable
attention in the radio research laboratories in the USA, especially those
concerned with the defence industry.
As an example of the fundamental nature of the vector potential, in the
last few years there have been a number of papers in the American journals
from research labs and defence consultants concerning contra-wound toroidal
antennas. By superimposing a toroidal coil with a left hand thread upon a
toroidal coil with a right hand thread one can cancel out the magnetic
field but the torus still radiates with no magnetic field within it or
escaping directly from it. This trick, which I originally demonstrated
with a reflecting plate superimpopsing an inverted image on the torus, but
can be done directly at very low power level by winding a left handed
toroid on top of one with a right hand thread, clearly demonstrates that
only the vector potential is required for radiation, vide the current
American litterature in particular an early paper by Carron, N.J: American
Journal of Physics,1995, 63, pp 99-103, Carron was unaware of my
experimental work at the time.
Mathematically it all makes simple sense because one can derive all of
Maxwell's equations from the curl and the divergence of a single property,
the vector potential. Incidentally this immediately shows that, even the
lowest frequencies, radio radiation is quantised, ie in separate photons a
few miles long, but that is another story which I am hoping to publish
elsewhere, but see an introduction in Jennison, R.C: I.E,E proceedings -
Microwaves, Antennas and Propagation, Vol 146,Feb 1999 pp 91-93 (but note
an error in draughtmanship in Fig 1 where the plus and minus signs on the
right side of the diagram appear in the wrong order, they should coincide
with those on the left)!
All of this may seem to be a bit too theoretical because one cannot
actually see the vector potential, one only observes the effects of its
presence, but, after all, the same applies to magnetism. One never
observes a magnetic field, - only the effects that it produces. However,
radio hams tend to be very practical people so how does this vector
potential behave in practical circumstances? A few weeks ago I
constructed a device to put it to the test. The effect of the earth
swallowing up an observeable proportion of the transmitted power tends to
appear below about two megaHertz, so I tried an experiment on 'top band'.
I designed an antenna only 40 cms in diameter which relied almost entirely
upon the emmision of vector potential and was only 2 feet above the ground
with a series of small metal plates (tobacco tin lids) and eight tiny coils
all confined within the same diameter of 40 cms. A two metre co-axial
cable connected this curious antenna to the TX. When I tried it out I
received reports on my ssb transmission in excess of S5 from all parts of
the UK (i.e. over 500 kMs from my QTH in Canterbury.). I am now in the
process of constructing a somewhat similar (and more expensive!) version to
try on the LF bands - just to prove the point.
For the benefit of any other readers the term CURL just means that the
entity travels in a curved track and the DIVERGENCE means that it sprays
out in the manner of the spreading fine streams of water from a rose on a
watering can or garden hosepipe. It may be of interest to note that a
curling vector cannot diverge at the same time so that in any circumstances
where they appear to do so one is actualy dealing with a cluster of
independent vectors - e.g. photons, but more of that later!
73, Roger, G2AJV.
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