What happens when the frequency of AC is very high?

[Dr_Nate]

If the capacitor contains a dielectric, though not with a vacuum, I would have expected electrons to be moving back and forth in response to the applied electric field, constituting an electric current.

Yes, this is true.

If so, the number is trivial compared to the actual current in the circuit. If there are very many, you would be having dielectric breakdown.

The numbers are comparable. The electrons don't need to move far in an oscillation. Dielectric breakdown occurs because the electrons are ripped from their ions; this usually occurs due to a large voltage.

Just to be difficult, I could point out that any net movement of charge through a metal conductor with a high frequency AC would be more or less the same as the movement of charges when the molecules in a capacitor's dielectric are polarised cyclically.

In a sense, you are right. The free and bound charges contribute to the AC conductivity $\sigma(\omega)$ in the generalized form of Ohm's rule: $\vec J(\omega)=\hat \sigma(\omega)\vec E(\omega)$. If I measured the conductivity at a single frequency, I wouldn't know how much was from free charge and how much was from bound charge. But, if I knew the conductivity over a large range of frequencies, I can see characteristic shapes in the graph due to bound and free charges.

 

[hilbert2]

I guess I would describe a capacitor as any element in a circuit that doesn't pass DC current, so I guess a simple hand operated switch becomes a capacitor in the off position.

Almost anything that fits this description probably has a capacitance, but it doesn't tell what makes something a good capacitor and something else a bad one.

 

[Dr_Nate]

The question related to extremely high frequencies and whether an electron executed SHM. I respect people's explanations here (I am outgunned and outnumbered), but find it easier to consider that it has this motion, in both conductors and dielectrics, superimposed on a large thermal motion. Further, for conductors, the SHM is disturbed by collisions, hence we see shot noise accompanying the signal.

I should correct something I said. Earlier I described electrons as following simple harmonic motion when discussing the Drude and Lorentz models. I should have called it damped-driven harmonic motion, which is what the Drude and Lorentz models model. I know this very well, but I just used the wrong words.

The difference is that a simple harmonic oscillator will freely vibrate at one frequency, whereas we are using an alternating field to drive the oscillations and there is also a mechanism to dissipate this energy. The response of the oscillator then has a shape of a Lorentzian function.

You are pretty much spot on, if you replace SHM with damped-driven harmonic motion.

Graduate students of solid-state physics are taught exactly this. You can see it in the notes of the late Millie Dresselhaus: http://web.mit.edu/course/6/6.732/www/6.732-pt2.pdf.

 

[Dr_Nate]

The ideal mass-spring system consists of a particle of mass $m$ attached to a spring with spring constant $k$. The frequency is $\omega=\sqrt{\frac{k}{m}}$.

What happens to the speed of the particle as $\omega$ increases beyond all bounds?

I can probably help you, but I don't understand your question.

 

[rzyn]

The magnetic field arises as the electric current vector changes. The AC could not be transmitted without an alternating magnetic field. As electric currents and magnetic fields alternate at higher frequencies, more of the energy is transmitted down the wire in the form of changing magnitudes than in the magnitudes themselves. It doesn't really matter how far the charge carriers travel. Building and collapsing a tiny magnetic field really fast can transmit as much energy as building and collapsing a large one slowly.

At sufficiently high frequencies the impedance of the conductor is so high the waves reflect off. That's why you can't use copper as a fiber optic cable. You can shine light on copper, and the electrons move, but the wave bounces off.

It's not so much that the electron drift reduces to zero at sufficiently high frequency as it is that transmission down the wire ceases.

 

[artis]

@phinds I agree an incomplete description but then again capacitance forms literally everywhere when we look, in fact I have made many mistakes in the past making pcb circuits without keeping this in mind.As for the capacitor's and dielectrics and current, I guess the "better" the dielectric the more polarization current will there be in it, so for high dielectric constant materials (some exotic materials up to 10 000K) the current could indeed be considerable or comparable as @Dr_Nate said earlier.

 

[jbriggs444]

The ideal mass-spring system consists of a particle of mass $m$ attached to a spring with spring constant $k$. The frequency is $\omega=\sqrt{\frac{k}{m}}$.

What happens to the speed of the particle as $\omega$ increases beyond all bounds?

Surely, that depends on what you are holding constant as you alter $k$, $m$ or both to affect $\omega$. If you are holding the speed of the particle constant then it does not change.

If you imagine a plucked violin string pulled to a fixed displacement then, as string tension increases without bound, string velocity at the zero displacement point increases without bound.

If you imagine a hammered piano string struck with a fixed energy then as string tension increases without bond, string velocity at the zero displacement point remains unchanged.

[And if you ramp up the tension on an already-excited string without damping then it depends on details of the tightening, but I believe that the typical case is that string velocity at the zero displacement point increases without bound. Without solving (or stating) the recurrence, it is also plausible that a finite bound is approached]

 

[StandardsGuy]

The electron doesn't have a diameter.

That is in dispute: diameter of electron

 

[vanhees71]

There's nothing to dispute about. It's pure "science fiction" no science

 

[tech99]

At sufficiently high frequencies the impedance of the conductor is so high the waves reflect off.

But copper reflects waves at low frequencies just as well, and there is no lower limit. For instance, the ground screen of a VLF transmitting antenna.

 

[Dr_Nate]

@phinds I agree an incomplete description but then again capacitance forms literally everywhere when we look, in fact I have made many mistakes in the past making pcb circuits without keeping this in mind.As for the capacitor's and dielectrics and current, I guess the "better" the dielectric the more polarization current will there be in it, so for high dielectric constant materials (some exotic materials up to 10 000K) the current could indeed be considerable or comparable as @Dr_Nate said earlier.

You are quite right about capacitance. Any two separated metals will have a capacitance between them, but strengths will differ greatly.

I can see why you thought I was talking about currents, but I was referring to the number of electrons. You are right to think that the magnitude of the polarization current will be dependent on the material.

I do think you are making a bit of a mistake when you say 'current' or phinds says 'actual current'. This sounds like you are referring to a DC current. I believe in post #18, tech99 was only talking about an AC current.

 

[Dr_Nate]

But copper reflects waves at low frequencies just as well, and there is no lower limit. For instance, the ground screen of a VLF transmitting antenna.

He didn't mention that a small portion of the wave is transmitted (and probably absorbed). If you look up RL circuits you will find you can make a low pass filter with a resistor and an inductor.

I think at this point a lot of us are cross talking because we aren't talking about a single precise circuit or material and how we are measuring it.

 

[sophiecentaur]

Any two separated metals will have a capacitance between them, but strengths will differ greatly.

How can that be true? The Impedance of a metal plate is very low and not dominated by permittivity. The impedance of the gap is very high and will dominate the situation.

 

[davenn]

Any two separated metals will have a capacitance between them, but strengths will differ greatly.

How can that be true?

EG, any two wires, PCB tracks have mutual capacitance between them. and increasing the freq. makes the effects worse
But you should already know that

 

[sophiecentaur]

EG, any two wires, PCB tracks have mutual capacitance between them. and increasing the freq. makes the effects worse
But you should already know that

Your statement implies that the metals make a difference. It's the geometry and the dielectric that count.

 

[Baluncore]

Going all the way back to post #1; I see …

If I change the frequency to 1Hz, the current will flow left to right for 1 second and then right to left for 1 second.

That is incorrect. One second in each direction is a frequency of 0.5 Hz.
For 1 Hz, the current would repeat with a period of one second, so it would flow for half a second in each direction.
The frequency f in Hz is related to the period T in seconds by f = 1 / T.

For a current of one ampere, one coulomb charge of electrons will pass any fixed point on the conductor per second. The distance the electrons travel in one direction before reversing is proportional to the period of the waveform. For higher frequencies, the period and the distance traveled become less, but whatever the frequency, for the same current, the same number of electrons pass any point on the conductor per unit time.

The equation and graph of; F = 1 / T; is asymptotic to both axes. Neither the frequency nor the period can be zero, the graph simply doesn't go there.
The turn on transient of a DC current makes it the start of an AC current that will change sometime in the future. It may have a very long period, but it can never have zero frequency.

 

[davenn]

Your statement implies that the metals make a difference.

not at all, and if that is what you read, then you misunderstood, I made no mention of metal types or the dielectric type
I just stated an eg., (example) of mutual capacitance and its effect as freq increases.

 

[sophiecentaur]

if that is what you read, then you misunderstood,

Ahh, I see the problem. I should have been replying to @Dr_Nate . Sorry for the misunderstanding.

 

[Dr_Nate]

Ahh, I see the problem. I should have been replying to @Dr_Nate . Sorry for the misunderstanding.

I don't follow how my statement implies that the metals make the difference. When I said the strengths differ greatly, I was referring to the capacitance, which as you mentioned depends on the dielectric and the geometry.

 

[sophiecentaur]

I don't follow how my statement implies that the metals make the difference.

It's because the only possible variables you mentioned were the "two metals". If you had used the word "capacitance" or mentioned geometry or dielectric then there would have been no problem. Readers are not mind readers.

 

[Dr_Nate]

It's because the only possible variables you mentioned were the "two metals". If you had used the word "capacitance" or mentioned geometry or dielectric then there would have been no problem. Readers are not mind readers.

But, I did say capacitance twice and quoted somebody talking about parasitic capacitance in PCBs

 

[Paul Colby]

On the other hand, a vacuum capacitor does not radiate.

I'm baffled by this. One can make a patch antenna without dielectric[1] and it will radiate because an aperture field is still present. The same radiation integral would be used with or without a dielectric.

[1] one would support the patch above a ground plane with the feed wire.

 

[ThatGuyIS]

Summary:: How is the motion of electrons in very high frequency AC?

If I consider a wire carrying AC current, I know that at an AC frequency of 0Hz, the current will always in the same direction. If I change the frequency to 1Hz, the current will flow left to right for 1 second and then right to left for 1 second.

I guessed that at these higher frequencies, as the voltage is the same, the velocity of the electron will not increase but the time period will decrease, so an single electron will move in an SHM whose amplitude will decrease as frequency increases. If this is correct, what will happen as the frequency becomes extremely high? Does the electron become stationary?

Shoot off a quick burst of EMP and see what you get...

Speed is the distance traveled by an object where as, velocity is distance traveled by an object per unit time in a particular direction. I think it’s a logic problem with definition.

 

[tech99]

I'm baffled by this. One can make a patch antenna without dielectric[1] and it will radiate because an aperture field is still present. The same radiation integral would be used with or without a dielectric.

[1] one would support the patch above a ground plane with the feed wire.

If a capacitor has only vacuum between its plates, where is there an accelerated charge to cause radiation? In the case of the patch, it often is used as a slot antenna, four slots being formed around the edges of the patch. With slot antennas, it is the acceleration of the charges on the metal which do the radiating. It is also possible to have radiation from the feed wire.

 

[Paul Colby]

If a capacitor has only vacuum between its plates, where is there an accelerated charge to cause radiation? In the case of the patch, it often is used as a slot antenna, four slots being formed around the edges of the patch. With slot antennas, it is the acceleration of the charges on the metal which do the radiating. It is also possible to have radiation from the feed wire.

You've answered your own question, in the capacitor plates and feed wire. A free standing parallel plate capacitor fed with a harmonic current will radiated, there will be an aperture field present around the edge of the plates.

This entire thread has had a fixation on charges and their motions. From a radiation/current flow perspective it's quite reasonable to approach all these problems from a classical boundary value problem approach where $J = \hat{n}\times H$ is taken as the surface current for example. That's not to say there isn't significant physics in the conduction of charges, however, for many (dare I say all) one need not do so as these effects are accounted for as material constitutive relations.