Hi Jim,
As always you ask good questions. Regarding the first one, though...
Could you please explain in more detail the relationship of the
electromagnetic wave, that travels in the space outside of the
conductor, (At near the speed of light), and the "current" that travels
very slowly slightly vibrating back and forth at 60Hz in the conductor.
... I'm not sure what I can add to what I said in my long post above dated 8-23-2017 at 7:08 p.m. EDT.
Regarding your other questions:
From what I understand the movement of the current in the conductor is quite slow.... Correct?
Correct, assuming "current" is defined as the movement of charge carriers (i.e., electrons in a metallic conductor). An example described in the Wikipedia writeup on
Drift Velocity indicates that for a current of 1 ampere in a copper conductor of 2 mm diameter the velocity calculates to 23 um/second ("um" = millionths of a meter). As noted in the writeup, btw, random movement of electrons even in the absence of "current" occurs at a far greater velocity (the Fermi velocity) than the "drift velocity" of current, although the Fermi velocity is still vastly slower than the speed of electromagnetic wave propagation.
Am I correct in saying you can’t have the electromagnetic wave without having current?
Yes, in the case of electrical energy that is being conveyed via wires. Electromagnetic waves can of course propagate in free space, as in the cases of radio waves and light waves.
The bigger the load, the more current in the conductor. The more current
in the conductor the larger the electromagnet wave.... Correct?
Yes, assuming "larger" is interpreted in the sense of having "more energy."
IF the wire is too small to handle the amount of current in the wire is
it the current that causes the wire to overheat or is it the energy of
the electromagnetic wave? Please explain in detail.
The Poynting Vector, which describes the direction in which energy is being propagated, would be perfectly parallel to the conductor if the conductor's resistance were zero. Since that resistance is non-zero, the Vector will tilt slightly toward the conductor, resulting in a small amount of energy being transferred into conductor, absorbed by its resistance, and converted to heat. In effect, the resistance of the conductor causes it to become part of the load.
... if only a voltage, (potential), is present, an electromagnet field will
exist outside of the conductor/s without there being current... Correct?
I'm not 100% certain, but I believe in that situation an electric field would be present, but not a magnetic field.
I know it is the energy, from the electromagnetic wave, that makes a
heating element heat up and gives off its’ heat into the surrounding air
around it. It is not the "current" directly causing the resistance
element to heat up.... Correct?
As I've said, in the case of electrical signals (or power) being conducted via wires the electromagnetic wave and "the current" go hand-in-hand, and one would not exist without the other. So the question is essentially just an academic/philosophical one IMO, not unlike the classical question of whether the chicken or the egg came first.
Your succeeding statements involving E, I, P, etc. are of course correct.
herman said it is the energy of the electromagnetic wave passing on the
outside of the fuse element link that causes it to melt and blow open
when the fuse is overloaded.
It is energy absorbed **from** the electromagnetic wave by the non-zero resistance of the conductor in the fuse, which as I said causes the Poynting vector to tilt slightly toward the conductor, that causes it to blow.
Is not P the energy of the electromagnetic wave?
They are proportional, but strictly speaking energy corresponds to power x time.
Here is where I get hung up. As you know a 2 amp 250V fuse can be used
for any voltage 250V or less. It could be used where the voltage is 24V.
The ampere rating of the fuse is still 2 amps. So to me the current has
to be some component that causes the fuse to blow when the current that
passes through the fuse link and exceeds 2 amps in the time curve set
by the fuse manufacture. NOTE I did not say current flow.
In my earlier long post I defined "the current" as follows:
What can be referred to as "the current," as opposed to "the signal,"
can be considered as corresponding to the number of electrons traversing
a given cross-section of a conductor in a given amount of time. One
ampere of current, for example, corresponds to one coulomb per second,
where one coulomb corresponds to the amount of charge possessed by about
6.2 x 10^18 electrons.
Since the amount of energy that is absorbed from the electromagnetic wave by the conductor in the fuse and converted into heat (causing it to blow if excessive) is proportional to both the energy that is being conveyed by that wave and to "the current," it is reasonable (and of course far more practical) to analyze the situation in terms of amperes and ohms, rather than in terms of joules (a unit of energy) and Poynting Vectors.
And correspondingly, since in the case of electrical signals (or power) being conducted via wires the slow moving "current" and the very fast moving electromagnetic wave go hand-in-hand (as I've explained), IMO it would be meaningless to think of one but not the other as being the cause of the fuse blowing.
Best,
-- Al