On Dec 3, 9:10*pm, tom wrote:
Art Unwin wrote:
Of course one can go back to the basics of mathematics way back in
Arabic times where
the mere presence of an equal sign denotes equilibrium or balance. The
equal sign is part of Maxwells equations so equilibrium is in effect.

"the mere presence of an equal sign denotes equilibrium or balance"

So sayeth the master of the physical universe - Art Unwin...

Hmmm, so if there is an equal sign, it means it's in equilibrium.

So a half wave antenna = 468/f(Mhz).

It is therefore in equilibrium.

tom
K0TAR

The book what you read lied to you!
When you look at a sinosoidal curve the area above and below the datum
line is never equal ! If it were you have invented perpetual motion.
Power is continually being injected to make up for frictional
losses incurred. After a full cycle you get to what is a repeatable
point termed as a period where you have adjusted the energy contained
to equal that of the beginning. With the areas not being equal because
of frictional losses the curve crosses the datum line at a point not
at the half way point of a period. This point is resistive, where as.
if you put it next to the true half way point you would see that the
points were not one and the same. This sequence of events is that of a
"tank circuit"
which you would learn about if you went to college!
Resonance is the point where the curve is totally resistive only and
it does not represent a point of equilibrium. A period or a FW point
is also totally resistive and in a state of equilibrium, a point of
repeatablity which the half wave point does not
When dealing with the laws of Maxwell, which includes an equal sign,
metrics used are only those that represent equilibrium which, in the
case of radiation requires multiples of a full wave (FW) where the use
of the half wave would nullify the equal sign and the whole equation
No where does Maxwell's equations suggests a particular shape or
elevation or even straght when describing a radiator, only that it is
at a state of equilibrium. Thus a radiator can conform to Maxwell's
equations when totally compressed to a point source which certanly
would not require a reflector representing a straight length of the
magnitude you have stated.
Note also that Maxwells equations refer to distributed loads only and
not lumped loads which, if present, MUST therefore be canceled.
Art Unwin KB9MZ....xg (uk)
Hopefully you are now back on track with respect to the science of
radiation.