ljcox:
Well, the professor came right out and stated that current does not flow through a capacitor, and although he was tempted to say that it did, he always corrected himself. Why would he have to correct himself if it was ok to say that?
Because he imprecisely said "...current does not flow through a capacitor...", when what he really meant was "...
conduction current does not flow through a capacitor..."
Most of the dispute in this thread seems to me to derive from lack of proper, precise, terminology.
The word "current" is often being used without qualification. If the disputants would always say "conduction current" or "displacement current", as appropriate, and not just "current", much of the disagreement could be avoided.
In this article:
Displacement current - Wikipedia, the free encyclopedia
the first paragraph under the heading "Current in Capacitors", contains the statement "Although
current is flowing through the capacitor, no actual charge is transported through the vacuum between its plates." The next two sentences say "Nonetheless, a magnetic field exists between the plates as though a
current were present[/COLOR] there as well. The explanation is that a
displacement current ID flows in the vacuum,"
These three sentences exhibit the problem with imprecise terminology that I'm talking about.
The first use of the word "current" is without qualification and it is asserted to flow even though no charge is transported; later we are told that what was meant was "displacement current".
The next use of the word "current" is in the phrase "as though a
current were present". In this case the author apparently means "conduction current", a current consisting of charge transport. If he meant the same thing as he meant by "current" in the first sentence, he wouldn't have had to say "as though a current were present". He should have said "as though a
conduction current were present"
A theory of everything is not necessary to settle the issue of whether "...a current can only be defined as a flow of charge carriers". It's not a matter of theory; it's a matter of semantics.
Maxwell's equations give us the answer to any (non-relativistic) question about how electricity behaves.
For the issue at hand, the equation:
[latex]\oint H \cdot dl = I + \frac{\partial \Phi_D}{\partial t}[/latex]
tells everything we could want to know. This equation provides a definition of "current" as the integral of H dot dl. In other words, we integrate the magnetic field intensity around a closed curve and that will be the value of the "current" passing through a surface bounded by the curve. The equation tells us that there may be two physical processes contributing to the magnetic field--a transport of charge carriers or an electric field which is changing in time. We could choose to use the unqualified word "current" to represent the integral of H dot dl. We could use qualified words to represent the two component parts of the "current", such as "conduction current" and "displacement current".
So, if we want to know the current passing through a region of space bounded by a closed curve, for example the circumference of a round wire, or a curve surrounding the space between the plates of a vacuum capacitor, we need only provide a means of measuring that integral. The tongs of a clamp-on ammeter do just that. If we could have a really small clamp-on ammeter that could enclose just the space between the plates of a vacuum capacitor, it would measure the (generalized) "current" (more precisely the "displacement current") passing "through" the capacitor.
It's a mistake to assume that in a conductor the [latex]\frac{\partial \Phi_D}{\partial t}[/latex] component doesn't exist. Except in a superconductor there is still a "displacement current" component; it may be very small, but it is there. In resistive materials the "displacement component" may be substantial; in a near vacuum it will be dominant and in a perfect vacuum it is all there is.
Maxwell chose to call the [latex]\frac{\partial \Phi_D}{\partial t}[/latex] component current "displacement current" because he believed in the "aether" and a "sea of vortices" interpretation of the "electric fluid". It was an unhappy choice for us. Perhaps less confusion would result if it were called something like "virtual current".
A similar situation exists with the choice of the name "imaginary" for one of the components of a complex number; the name causes consternation.
This "displacement current" phenomenon shouldn't be as puzzling as it apparently is. It is an experimental fact that with a time-varying electric field is associated a magnetic field, and with a time-varying magnetic field is associated an electric field.
The latter phenomenon should seem just as mysterious, but it's greater familiarity in everyday experience has robbed it of most of its mystery.
What I'm referring to is this: imagine a two foot long piece of 10 gauge magnet wire. This wire has a resistance of about 1 milliohm per foot. Further imagine that you connected the probes of your voltmeter across the ends of the piece of wire and measured 1 volt AC @ 60 Hz. You would probably say that there must therefore be a current of 500 amps flowing in the wire; how else could there be a 1 volt drop across a big copper wire like that?
[latex]\oint E \cdot dl =- \frac{\partial \Phi_B}{\partial t}[/latex]
The right hand term of this equation should perhaps be called the "displacement voltage".
A closed curve surrounding a region of space wherein there is a changing magnetic field will have an electric field along it which will integrate to a non-zero value. That non-zero electric field will be able to produce separated charge in a conductor.
What I'm describing is a situation where the 10 gauge wire is wrapped a few times around a magnetic core, a transformer core where the primary is energized by a 60 Hz line voltage. In this situation the wire can have a 1 volt difference between the ends of the wire even though there is no current in the wire. Why don't we think that is mysterious? The ends of the wire are points between which there is a 1 volt difference, and the resistance between those two points is .002 ohms. Why isn't there a 500 amp current between the ends of the wire? Isn't that mysterious?