K7ITM wrote:
Hmmm...this is getting back really close to what I was trying to get at
when I posted the capacitance-of-a-wire-conundrum basenote a few weeks
ago that went nowhere. But since you've opened it up again, I'll toss
out some conundrum-ish things about it.

Consider a wire that's perpendicular to a ground plane; obviously this
is interesting for a doublet configuration also, because of symmetry.

I believe I can, without too much trouble, find the inductance of a
cylinder of current--current in the shallow skin depth of the wire,
which is different than the inductance at low frequencies--per unit
length. I believe it will be relatively unaffected by distance along
the wire.

I believe I can, with a little more difficulty, find the (DC, as you
say) capacitance to the ground plane of a section of wire that's short,
in isolation from the rest of the wire (as if the rest of the wire
weren't there). But I believe that capacitance will be a much stronger
function of distance from that short section to the ground plane than
was the case for inductance.

That leaves me with a velocity, sqrt((capacitance/unit
length)*(inductance/unit length)), that is not particularly constant
along the length of wire. I know that things really are like you say:
the velocity along that wire will be nearly the speed of light.

So that tells me that something is wrong, and three things come
immediately to mind: either the inductance is more variable with
distance from the ground plane than I think it is, or the capacitance
is less variable, or the DC analysis does not hold when we are dealing
with things propagating at about the speed of light.

In fact, there is a clue in the fact that for the whole wire, with one
end spaced a very small distance from the ground plane and the other
end far away, in a DC case the charge would be clustered near the
ground plane, with very little charge at the tip...but in a resonant
antenna, there is often a LOT of charge out near the end that's far
away from the ground plane.

OK, that ought to be enough to get lots of conflicting responses going!

Cheers,
Tom


What is the transmission mode in a single conductor transmission line?
Does a coil support TEM waves, TM, or TE? Is there some type of
cutoff frequency?
How do you compute the phase velocity? How do you know the phase
velocity of an electromagnetic wave on a coil of wire isn't greater
than the speed of light in the helical direction?
People like Reg and Cecil like to simplify things to the point of
absurdity. Things that complicate the picture and disagree with their
simplifications are promptly ignored. I hope no one reading these posts
is under the false impression he's learning transmission line theory.
73,
Tom Donaly, KA6RUH