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OfflineAnnomM
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Faraday cage and different EM frequencies
    #10328144 - 05/12/09 06:22 PM (12 years, 5 months ago)

Is there a relative simple explanation for the interaction of a Faraday cage with different electromagnetic radiation frequencies? In other words, why does visible light pass through the Faraday cage in a microwave door and microwaves not?

I'm looking for a better answer than "visible light has a higher frequency". Anyone?


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Re: Faraday cage and different EM frequencies [Re: Annom]
    #10328186 - 05/12/09 06:33 PM (12 years, 5 months ago)

The spacing of the mesh.
Light's wavelength is significantly shorter than the spaces between the mesh. Microwaves are much longer wave, and get caught by the mesh.


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OfflineAnnomM
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Re: Faraday cage and different EM frequencies [Re: Doc_T]
    #10328227 - 05/12/09 06:44 PM (12 years, 5 months ago)

Yeah, thanks, but I'm looking for the mechanism of the "getting caught by the mesh".


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Re: Faraday cage and different EM frequencies [Re: Annom]
    #10328329 - 05/12/09 07:04 PM (12 years, 5 months ago)

I always figured it was a quantum thing. If the wavelength is like 10x the hole size, then you have a 1/10 chance of getting out. Or something along those lines. Probably goes up as the square of the difference.


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OfflineSeussA
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Re: Faraday cage and different EM frequencies [Re: Annom]
    #10328440 - 05/12/09 07:30 PM (12 years, 5 months ago)

> I'm looking for a better answer than "visible light has a higher frequency". Anyone?

It is fairly complex.  The general rule is that you want the mesh size to be much smaller (1/50th) than the wavelength you wish to block.  Depending upon the frequency you are wishing to block, the material that your cage is made from, and the grounding of the cage, (among other factors), the distance within the cage that the E/M field attenuates will be different.

Basically, the cage absorbs the E/M and then re-radiates it at a much lower strength.  Analysis is difficult because things as small as soldier joints in the cage can effect current paths, acting as a large impedance discontinuity at high frequencies, causing the cage to more or less become an antenna.

In a nutshell, the smaller the hole the less energy passes through it, thus the smaller the re-radiated field on the other side.


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Re: Faraday cage and different EM frequencies [Re: Annom]
    #10328452 - 05/12/09 07:33 PM (12 years, 5 months ago)

Quote:

Annom said:
Yeah, thanks, but I'm looking for the mechanism of the "getting caught by the mesh".





Yeah I never got it either, basically.
My understadning is that since EM waves are transverse waves that the location of the wave actually physically does change in the y and z direction (if x is the direction of propogation) over every oscillation.  The extent of this oxcillation in the y and z direction should be a function of the wavelength.  Obviously, the greater the oscillation in the y and z directions the more room they need, and if thats greater than the available space in the faraday cage, the wave will hit the metal and do its thing.



Make sense?


Hopefully someone can tell me if I'm correct or not, but I believe its cuz the "height" of the wave is a real phenomena and not just a representation of magnitude in those pictures of the sine waves propogating they always show.



Like I said, I'm not confident in this answer, but that's what I've thought, I'd love to hear more about this from someone who knows more.  The math doesn't really answer the questions conceptually in many cases- at least the math I've had to do for school.


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Re: Faraday cage and different EM frequencies [Re: johnm214]
    #10328523 - 05/12/09 07:50 PM (12 years, 5 months ago)

Quote:

The extent of this oxcillation in the y and z direction should be a function of the wavelength.




No, I think the extent (or amplitude) of oscillations is proportional to the intensity (or the number of photons squared).  This should not effect whether or not an EM wave can penetrate a Faraday cage.


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Re: Faraday cage and different EM frequencies [Re: DieCommie]
    #10328593 - 05/12/09 08:03 PM (12 years, 5 months ago)

Ok, but the height is actually a real height right?  The wave is actually going up and down- moving in more than the direction of propogation, correct?


yeah, but say for one photon only, so no interference at all.  What is the "height" (in the y or z directions) a function of?  Is the wavelength irrelevant?  What causes the farady cage's dependance on wavelength?


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OfflineSeussA
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Re: Faraday cage and different EM frequencies [Re: DieCommie]
    #10328606 - 05/12/09 08:05 PM (12 years, 5 months ago)

Better to look at using Gauss' law.


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InvisibleDieCommie

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Re: Faraday cage and different EM frequencies [Re: johnm214]
    #10328700 - 05/12/09 08:29 PM (12 years, 5 months ago)

Quote:

johnm214 said:
Ok, but the height is actually a real height right?  The wave is actually going up and down- moving in more than the direction of propogation, correct?




The height represents only the electric field.  There is not a point-like photon moving in a wave fashion.  What is oscillating is the magnitude of the electric field.  The magnitude of the electric field is a property of a point in space only, it does not extend to other points. 

Say a wave is centered on (x,0,0).  Now at that point there is an electric field and it has a magnitude of say 2, thats just the value in that point in space.  It is not an actual thing that extends two spots over into (x,2,0).  Now that value increases and decreases sinusoidally with time and that is the wave. 

In addition to that point in space having a magnitude of electric field, it also has a direction of course, that you see pictures like this...

http://hyperphysics.phy-astr.gsu.edu/hbase/images/emwv.gif

Now just apply what you know about vectors to this picture.  The arrows dont represent actual things in space, they represent magnitudes and directions at point of origin only.


Quote:

What is the "height" (in the y or z directions) a function of? 




Its a function of time, and it represents a magnitude of the electric field at that point.


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InvisibleDieCommie

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Re: Faraday cage and different EM frequencies [Re: Seuss]
    #10328708 - 05/12/09 08:32 PM (12 years, 5 months ago)

Quote:

Seuss said:
Better to look at using Gauss' law.




hmm, dont follow.  Use it how and for what?


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Re: Faraday cage and different EM frequencies [Re: DieCommie]
    #10328784 - 05/12/09 08:53 PM (12 years, 5 months ago)

Hm interesting question.

When we derive results in the case of a perfect conductor of course we get that the Electric Field is zero inside the conductor.  If we start poking holes in the Conductor than any EM wave that varies quickly enough such that the area of metal around is not enough to screen the field would be able to get out.  So for instance in a microwave, microwaves can be blocked because they move slowly enough to effectively sense that it is a continuous surface.  Optical frequencies can escape because this approximation no longer holds and we are simply dealing with a discrete surface that cannot screen the fields.

Does this sound on the right path?  Ive never really thought about this before and as such Ill have to think about it before any math comes into play.

As for John's questions about photons, the Amplitude of the Electric Field is not a real thing in the way you are thinking.  Photons do not have amplitude, they have a fixed energy and momentum derived from Plancks relations.  Plane-wave solutions do not really exist in the real world, so a single photon cannot have a huge amplitude E_0 like you get out of Maxwell's equations.  You can have a wave-packet however with a high intensity however as I think Qubit pointed out this is not the same thing as what you are referring to.


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OfflineChuangTzu
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Re: Faraday cage and different EM frequencies [Re: Chespirito]
    #10328827 - 05/12/09 09:02 PM (12 years, 5 months ago)

It also helps to think of the wavelength of light not as the crest to crest distance of a classical wave but as the de Broglie wavelength of the individual photons.  Looked at in this way, you can see that photons with shorter wavelengths will interact with less of a mesh of a given size than photons with longer wavelengths.  Less overlap in space equals lower probability for interaction.


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OfflineSeussA
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Re: Faraday cage and different EM frequencies [Re: DieCommie]
    #10331041 - 05/13/09 07:07 AM (12 years, 5 months ago)

> hmm, dont follow.  Use it how and for what?

I was thinking of the direction of the fields with respect to the direction of motion...


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Invisibledeimya
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Re: Faraday cage and different EM frequencies [Re: Annom]
    #10331109 - 05/13/09 07:50 AM (12 years, 5 months ago)

What you also want to look at is the properties of electrons in metals since what ultimately dictate which EM waves passes through and which doesn't is the interaction of these EM waves with the electrons of the metallic cage.

The principal property of interest is the plasma frequency of your cage. The plasma frequency is the frequency at which the dynamic of your electrons cannot follow the dynamic of EM waves, meaning if your electrons are excited at low enough frequency, they can easily respond to the incoming EM wave and start oscillating at the same frequency, thereby reflecting and absorbing the EM radiation and shielding what's beyond.

If on the other hand you excite electrons in a metal at higher frequency than the plasma frequency, the electrons will stop seeing the EM wave since they cannot respond any more to them. The metal becomes transparent to them.

Said otherwise, below the plasma frequency the electrons can resonate with the incoming EM waves and thus reflect and dissipate the energy as heat. Above the plasma frequency, electrons cannot resonate with the incoming EM waves as they are driven too fast by it, and therefore appear transparent to them.

This plasma frequency phenomenon has to do with a collective resonance of every electron of your metal at the same time. It's a bit like the resonance frequency of the centre of mass of the negatively charge gas of conduction electron oscillating around the centre of mass of the positively charge background of the metallic ions.

The meshing of your microwave oven should therefore be smaller than the plasma wavelength as to not interfere with these collective plasma oscillations.

Another interesting thing about the plasma frequency is that it explains the colour of metals. Copper is red because the plasma frequency is somewhere above the red frequency and thus reflects the red part of the EM spectrum. Silver is, well, silver because its plasma frequency is in the UV range, therefore reflecting all the visible spectrum and acting like a mirror.


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OfflineAnnomM
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Re: Faraday cage and different EM frequencies [Re: deimya]
    #10332360 - 05/13/09 03:15 PM (12 years, 5 months ago)

Thanks all for the replies! I sometimes help highschool students with their physics class, when their teacher doesn't know more than their book, and this was one of the questions someone asked me. I can answer most questions, but this one was really difficult. I think I can give them a general feeling of the concepts involved now although it still is very vague and complicated. I also do tell them when I don't understand things myself and how accurate my answer is so they don't get a wrong view of things.

I should find some time to do a more serious attempt to study the Feynman's lectures on physics part 2.


Edited by Annom (05/13/09 03:18 PM)


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Re: Faraday cage and different EM frequencies [Re: deimya]
    #10332381 - 05/13/09 03:20 PM (12 years, 5 months ago)

Yes but as far as I remember the plasma frequency is usual outside of the visible range.  I don't see plasmons coming too much into play here.  Interesting side note however, plasmons are being researched for use in Solar Cells.  If you take nanoparticles of gold and put it into your solar cell, for instance adding it to your solution before spin coating in organic solar cells, then the incoming light will excite plasmon modes within the gold.  You can generate surface plasmons this way which get trapped in a guided mode and can be harvested, (in a manner of speaking thats not really whats happening)


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Re: Faraday cage and different EM frequencies [Re: Chespirito]
    #10333682 - 05/13/09 07:44 PM (12 years, 5 months ago)

I may be wrong but I would rather say that it has everything to do with the plasma frequency. Plasmons are the most elementary quasiparticles of the electron gas formed by conduction electrons. As such, in most everyday cases, their interaction with EM waves accounts for most properties of metal-EM wave processes. Even in a classical theory of electrons in metals, the plasma oscillations is one of the first phenomenon you stumble on when subjecting your metal to an oscillating electric field. Incidentally both quantum and classical treatment agree in the limit of a large number of plasmons.

If I recall correctly, the plasma frequency of everyday metal is around the middle of the visible range or higher in the UV range. That's why you can mesh your microwave oven door without affecting its shielding effect since there's at least an order of magnitude between both wavelength. Microwave ovens operate at 2.4 ghz, that is at wavelengths of ~12 cm. The meshing may be composed of 0.5 cm holes. Hence, for EM waves in the microwave range, the oven door appears as a metal sheet with maybe 2/3 of the density of an opaque metal sheet, and therefore with a plasma frequency shifted sqrt(2/3) ~ 0.8 lower (the PF is proportional to the square root of the density), still well above the microwave range.

Or something like that.


Edited by deimya (05/13/09 07:57 PM)


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Re: Faraday cage and different EM frequencies [Re: deimya]
    #10336106 - 05/14/09 04:08 AM (12 years, 5 months ago)

Yea plasmons are quite important for a number of things, indeed they are quite useful.  I didn't mean to try and get into an argument over whether plasmons are necessary to the understanding of a Faraday Cage however.


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Re: Faraday cage and different EM frequencies [Re: Chespirito]
    #10336286 - 05/14/09 05:51 AM (12 years, 5 months ago)

No problem, it wasn't my goal either. I was just making myself more precise to give an idea of where my claims were coming from.


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