Derfy
Charge is a concept not to be confused with "A charge." Electrons carry charge.
Now if I have a conductor of fixed diameter and length, what happens as the EMF is increased? Is there a physical limit to increases? What happens as there is an increase? Is charge discrete or continuous?
Can we avoid circuit theory in this discussion?
BTW your explanation hit the issue square on.
Charge is a concept not to be confused with "A charge." Electrons carry charge.
Now if I have a conductor of fixed diameter and length, what happens as the EMF is increased? Is there a physical limit to increases? What happens as there is an increase? Is charge discrete or continuous?
Can we avoid circuit theory in this discussion?
BTW your explanation hit the issue square on.
Ed,
I'd rather *not* play 20 questions, so pretty please if you have a point you want to make, go ahead and make it before I start cracking open my Kittel/etc and throwing equations at everyone. 😉
As you well know, charge is made up of "a charge", so inherently it's discrete, but that's a relatively meaningless title until we get down to very small quantities of charge. (-1 Coulomb = 6.24150934(14)e×10 18 e-)
We treat time as continuous, and haven't yet been able to measure it at fine enough levels to say if it's ultimately a discrete or continuous variable (if that's even realistically possible). So current can be described as continuous.
More EMF (assuming near-DC) = greater current. There are a number of 2nd order material effects that will affect the linearity of the resistance of the wire. Certainly there's an upper bound at which the Joule heating and net electron flux (for larger objects the former) will work to physically destroy the wire.
I'd rather *not* play 20 questions, so pretty please if you have a point you want to make, go ahead and make it before I start cracking open my Kittel/etc and throwing equations at everyone. 😉
As you well know, charge is made up of "a charge", so inherently it's discrete, but that's a relatively meaningless title until we get down to very small quantities of charge. (-1 Coulomb = 6.24150934(14)e×10 18 e-)
We treat time as continuous, and haven't yet been able to measure it at fine enough levels to say if it's ultimately a discrete or continuous variable (if that's even realistically possible). So current can be described as continuous.
More EMF (assuming near-DC) = greater current. There are a number of 2nd order material effects that will affect the linearity of the resistance of the wire. Certainly there's an upper bound at which the Joule heating and net electron flux (for larger objects the former) will work to physically destroy the wire.
Ah you get it but I wanted to build the issue for the heathens.
So if I have a copper wire what determines the velocity of propagation of a signal. Taking the step that charges carry the signal.
So if I have a copper wire what determines the velocity of propagation of a signal. Taking the step that charges carry the signal.
You can always use this if you want to get in trouble: Velocity factor - Wikipedia
Or talk to JNeutron, we're definitely in his domain when it comes to pushing these limits.
Or talk to JNeutron, we're definitely in his domain when it comes to pushing these limits.
Misses the issue. Velocity of propagation in a conductor is based on the mean free path for the charges. That raises the issue of the variance from mean and the effect of conductor size to variance.
If we're talking about the propagation of an EM wave, though, then mean free path isn't exactly what matters (in an excess of free carriers, which is the case for the discussion at hand; we're not making nanowire-based structures and then freezing them out to LHe temperatures or colder)
Electron mobility, which drive conductance is dependent on mean free path. That's a loss factor (resistance). The dielectric generally dominates the propagation velocity down a cable:
Speed of electricity - Wikipedia
Electron mobility, which drive conductance is dependent on mean free path. That's a loss factor (resistance). The dielectric generally dominates the propagation velocity down a cable:
Speed of electricity - Wikipedia
Is it easier if we look at a single conductor of one meter length with one end connected through a switch to a battery and a resistor for a load?
When I throw the switch it takes about 30 nanoseconds for power to hit the resistor.
Now when I throw the switch that is a sharp step function. Is the power at the load just as sharp a step? Does the wire gauge have any effect on this.
Circuit theory would have L&C show a quick exponential ramp up and wave theory says no. What does your original answer predict?
When I throw the switch it takes about 30 nanoseconds for power to hit the resistor.
Now when I throw the switch that is a sharp step function. Is the power at the load just as sharp a step? Does the wire gauge have any effect on this.
Circuit theory would have L&C show a quick exponential ramp up and wave theory says no. What does your original answer predict?
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Huh? The topic of discussion has been around cable construction, as silly as it is, where propagation velocity is going to be constrained by the dielectric. And also this is entirely meaningless within the essentially DC bandwidth known as audio. Even respecting what jneutron cites about extremely small phase changes with frequency.
Prop velocity is determined by the product of permittivity times permeability.
For an unconstrained wire, it is proportional to L times C.
For a coax, it is related to the dielectric.
Jn
No. Vprop in not related to mean free path. If it were, superconductors and fully annealed 7 nines copper would be super luminal.
It is related to 1/(epsilon times mu).
Jn
We are going to disagree on this. I am not suggesting any propagation that is faster than light in any conductor.
Nor am I using the wave model for all forms of propagation.
Trying to look at the fringe effects.
You can call it "fringe" if you wish. However, the propagation velocity is well known. It is not about electron velocity within a conductor. It is the velocity that both an e and m wave of equal energy travel through a media.
Jn
Jn
Whether wave or circuit theory is the most appropriate tool would depend on how sharp is the step function when you throw the switch. This in turn depends on how the switch is made, how much it bounces, stray capacitance etc. If you want to play gedanken experiments then you have to be internally consistent in your assumptions.simon7000 said:
Mean free path for the charges (microscopic theory) merely helps set the conductor resistance (macroscopic theory). Don't try to set one against the other. The conductor resistance then comes into the signal propagation velocity (for low frequency or bandlimited signals) because it adds to the series impedance, and at really low frequencies it may dominate over the inductance.
A single conductor one meter length is incapable of delivering power.
Your example is very bad.😉
jn
Deja vu?
I would think a suddenly turned off current in an open wire loop would lose some power to radiation. I also see no ambiguity in something like a reed switch charged line pulse generator that happens to have a resistive load at the other end. EM alone solves the problem exactly.
As usual a properly posed problem does not care how you solve it.
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My only thought is some mixing of effects (and what causes them): e.g. in an infinitely sharp unit step function, the change in self inductance of the wire due to skin effect over infinite bandwidth would change the shape of the pulse on the receiving side.
It's a contrived example, but an effect nonetheless.
It's a contrived example, but an effect nonetheless.
Do I really need to mention the other end of the resistor returns to the battery?
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