Roy Lewallen wrote in message ...
....
No, all you're doing is showing that they have the same dimensions. It
just doesn't seem to be sinking in that having the same dimensions
doesn't make two quantities the same thing. I've tried with the example
of torque and work, but that doesn't seem to be having any effect. Maybe
someone else can present some other examples, and maybe, just maybe,
with enough examples the concept will sink in.

I'd think the best examples come from dynamic systems, because the EM
wave is dynamic. In fact, you can define mechanical impedances, too.
You can have a long row of masses connected by springs, for example,
and spring force may be analogous to current, and mass displacement to
voltage. In a sound wave, the mass is the mass of the air (or other)
molecules, and the springs are the intermolecular forces (or elastic
collisions in air, if you will). Generally to propagate a wave,
you'll find you have two "state variables" whose states are
interrelated by differential equations, and the (a) solution to those
equations results in the description of the wave. The propagating
medium often has very low loss, and is propagating much higher power
levels than it's dissipating. So the (uV/meter)^2/377 has the units
of power, but that's not a power that's dissipated as it would be in a
377 ohm resistor...it's the power (at that frequency, or in that band)
per square meter passing that point in freespace.

The same is true, for example, of power going down a transmission
line, though the transmission line is much more dissipative than
freespace (unless it's made with superconductors). It's also true of
power transmitted by a driveshaft in a car: the torque you apply to
the input end twists the shaft, and that twist propagates down the
shaft. Yes, you can have reflections at the far end because of
impedance mismatches too.

I think a related concept is the difference between static (potential)
and dynamic energy. Both have units of energy, but they are rather
different things.

....


Here we are again. Potential and voltage have the same dimensions, but
aren't necessarily equal. And as far as I can tell, "voltage potential"
is meaningless. To quote from Holt, _Electromagnetic Fields and Waves_,
"When the electromagnetic fields are static, as we shall see, the
voltage drop along a path equals the potential drop between the end
points of the path. Furthermore, these quantities [voltage and electric
potential] are also equal in *idealized* electric circuit diagrams, and
they are approximately equal in physical circuits, provided voltmeter
leads do not encircle appreciable time-changing magnetic flux." Pay
particular attention to the last qualification. When a time-changing
magnetic field is present, the voltage drop between two points depends
on the path taken, while the potential drop is simply the difference in
potential between the two points. So the voltage between two points in
an electromagnetic field can be just about anything you'd like it to be.

It took me a long time to properly internalize that. It's not just
time-varying magnetic fields that cause trouble, either. A
temperature gradient along the voltmeter leads can cause an EMF also,
for example. A reminder: Kirchoff's voltage law is NOT that the sum
of voltage drops around a closed loop is zero, but rather that the sum
of voltage drops equals the sum of the EMFs in the loop. One such EMF
is because of any time-varying magnetic field enclosed by the loop
(and therefore may be different if you move the leads), but others are
chemical and thermal (actually two distinct thermal types). Both EMF
(electromotive force) and voltage drop have the units of "volts", but
they are not the same thing. I do like the statement in terms of a
closed loop much better than thinking about it between two points,
because Faraday's law says only that there is an EMF in any closed
loop enclosing a time-varying magnetic field, and that EMF is
proportional to the rate of change of the magnetic field. It does not
say that the EMF is uniformly distributed, nor that it is in any one
place, only that it exists. And Kirchoff's voltage law gives us a way
to apply that EMF (and any other EMFs which may also be in the same
loop because of other things happening) and understand why we see
voltage drops around the loop. Ohm's law tells us a lot about how the
drops will be distributed, according to the resistances in each
portion of the path. Faraday's law applies whether there is a
conductor in the loop or not. If there is a conductor the whole way
around, the EMF will drive a current in it--and that current will
create a magnetic field to oppose the one creating the EMF.

Cheers,
Tom