Dammit. What Ring said. Here’s a better (well, more complete, maybe) discussion of current.
http://www.utsc.utoronto.ca/~tawfiq/phyA21/Notes/L3.pdf
I’ll repeat, though: applying a potential difference across a conductor forces a voltage drop, an electric field, and current inside the conductor. An ideal superconductor might be different, but hell, they’re weird!
For a superconductor, the electric field can be zero while current is flowing, since the conductivity is infinite. Presumably, there must be a transient, non-zero electric field while the electrons are accelerating (i.e., you turn connect the wire, and the electrons have to accelerate to keep the field zero), but I’m not a superconductor guru. The physics of the transient behavior in superconductors is probably very complicated, and possibly not fully understood yet.
Your reasoning sounds correct to me. Just looking at J = sigma * E, for a constant current, if conductivity increases, the E-field would decrease. However, I don’t think the logic for the superconductor works. Ohm’s Law breaks down in the superconducting regime, I believe, simply because conductivity = infinity at this point. I don’t have any information at hand on this though, so I could be mistaken.
If you looked at a graph of Voltage versus Current for a superconductor (slope would be resistance), Ohm’s Law doesn’t work below the transition point.
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Thanks Zen.
So let me see if I understand this correctly:
I hook a battery up to a resistor using #18 AWG copper wire. 500 mA flows. The electric field intensity is extremely small in the wires, while the electric field intensity is (relatively) large in the resistor and battery.
But what if I used superconductor wires instead of #18 copper? 500 mA would still flow. But now the electric field intensity inside the wires is zero. Therefore, there must be another mechanism responsible for current flow other than electric field in this situation. Perhaps the same mechanism is used when I’m using #18 copper??
I can’t anyplace that states it very clearly, but my impression is that superconductors do indeed have a zero electric field inside, and all of the current flows along the outside of the conductor – as if it were in an external electric field?
I’m beginning to wonder myself, now. Clearly there is an e-field in a normal conductor when voltage is applied and current is flowing, but is that what is actually driving the current? Experiments have been done in superconduction…well, here’s a quote:
From this article. (Bolding mine).
Clearly there is some additional mechanism at work, at least in the case of superconductivity.
Once the current is flowing, I would expect it to keep flowing by conservation of momentum. No forces are acting on the electrons (except for the their own e-fields, which keep each other in line), so they should keep moving ad infinitum, until some external force is applied.
When dealing with a load connected via superconductors you’re in effect connecting the load directly across the voltage source’s terminals, the SCs just float at the source voltage.
Also, as Nametag said all the current in the SC must be on the surface. The Meisner effect says that the B field in the conductor must be zero, and therefore Maxwell’s equations stipulate that the E field and the current density in the conductor must also equal zero.
The question I hear the most about this subject is “why don’t the accelerating charges radiate?”
But, in a region having lots of free charges like a metal it doesn’t take a lot of E-field to move them does it?
I’m on my way to becoming an EE…man, this stuff is so confusing. I thought an E-field was independed of a conductor. It exists between any voltage drop and its strength is based on the permititivity of whatever is between the voltage source and drain. For a battery, an E-field does exist between the terminals, but air is such high resistance that no current flows. When you attach a wire, the E-field doesn’t change, but you now provide a means for electrons to travel down the e-field.
Another way to say it is that all freely mobile charges move in the field around the terminals. The circuit model works because the conductors are where the overwhelming majority of the mobile charges are located.
Yes.
An analogy would be sliding a disk along a frictionless surface, versus a real surface. Unless you are continuously applying force to the disk, it slows down on the real surface. Once the electrons are moving, in a superconductor, there’s nothing to slow them down, so they keep moving. In a good conductor, they interact with its atoms, and eventually give up their momentum and energy. With the electric field present, they are continuously accelerating, and that acceleration is in equilibrium with the losses due to the electron-atom interactions, so you get constant current flow.
I think I’m beginning to understand it better now.
In order for electrons to flow through a normal conductor, an electric field must be present in the conductor. This field gives the electrons the force to overcome the collisions they encounter (i.e. the “resistance”). When there’s not much resistance, you don’t need a large E-field in order to generate a sizable current. In a superconductor the lattice does not present any obstacles to the electrons. Therefore, current can occur without the presence of an electric field.
Is that right?
I happen to be an elelctrician, but this is way over my head.
I work at a research facility that researches the use of AC and DC electricity. There are some rather bright fellows here. I think one of them is published and may have some patents and a doctorate in EE (if that`s possible). I shall pick some brains tomorrow and report back and try to add to the fun.
What exactly should I ask? Is the OP still open or are superconductors now involved?
Well I think we have it covered, whuckfistle, but thanks for the offer. What’s bothersome is that I’ve taken “EM field” and “solid state devices” classes, yet I’ve never acquired a “feeling” for what’s going on with these damn electric and magnetic fields. Whenever I come across a conductor with lots of current flowing through it, I just naturally assumed that there must be a large electric field inside the conductor. Alas, I have been mistaken. There’s probably a very small E-field in the conductor.
Thanks to everyone for helping me out here.
Yeah, I think you’ve got a handle on it now, Crafter_Man. Next up, plasma theory! 
I think you MSEE coworker is mistaken in saying that the electric field inside an actual physical conductor, other than perhaps a superconductor, is zero.
For example in reflection problems it is assumed that at the surface of the conductor the electric field is zero which calls for a reversed field vector traveling in the opposite direction to the incident wave.
However, in actual conductors the reflection isn’t 100% and the field penetrates the conductor. Alternating fields penetrate to a distance that is the same as the skin depth computed for AC currents in circuit theory (Chapter 6, Noise Reduction Techniques in Electronic Systems, Ott, John Wiley and Sons).
According to Fields and Waves in Communication Electronics, (Ramo, Whinnery and Van Duser, John Wiley and Sons) the current associated with an EM wave can be written in two parts, the conduction current and the displacement current. In space, the conduction current is nearly zero and all the “current” is displacement which is a term contributing to the curl of the magnetic field vector.
But in a conductor the displacement current is near zero and nearly all the current is by conduction.
The mathematics is right at the feather edge of what I have retained after 25 years of neglect and I wasn’t all that great at it even then either.
Just a minor nitpick, David Simmons. The EM field doesn’t just penetrate to the skin depth. The field strength decays exponentially. The skin depth is the depth at which the field strength has been reduced to 1/e, or about 37%, of the strength at the surface.
And another minor nitpick.The penetrating EM field is an evanescent wave and since in an evanescent wave the E and B fields are ninety degrees out of phase it cannot transport energy. The energy just sort of sloshes around.
Since were going to get right into it, I’ll add another one.
Conductors only act as conductors up to a certain frequency. Beyond that critical frequency, displacement current exceeds conduction current.
For some common materials, the frequency is:
Silver… 1.1x10[sup]18[/sup] Hz
Aluminium… 6.7x10[sup]17[/sup] Hz
Solder… 1.2x10[sup]17[/sup] Hz
Sea Water… 9x10[sup]8[/sup] Hz