# Classical explanation for microwave door shielding

• em3ry
In summary, the microwave door grate acts as a Faraday cage, which prevents radiation from passing through.

#### em3ry

Gold Member
What is the classical explanation for why the microwaves won't pass through the microwave door?

The grate in the window acts a sort of a Faraday cage preventing radiation from passing through. The wavelength of the microwaves need to be at least twice the the hole diameter for it to work properly.

dRic2, Dale, vanhees71 and 2 others
I know that. I am asking for the classical explanation.

Water waves would pass through an obstruction like that. Why don't electromagnetic waves?

hutchphd and Delta2
A classical explanation of a quantum effect is like asking for an explanation of chemistry in terms of air, water, Earth and fire.
But if it pleases you, envision the photons as particles that don't fit through the holes if they're too big.

davenn, russ_watters and sysprog
em3ry said:
Water waves would pass through an obstruction like that
No, I don't think they would, unless you made the holes really big.
You can do a web search for "waveguide beyond cutoff" or "shielding effectiveness of holes" to learn a bit about this.
Here's one paper that I chose at random, there are lots of others.

Dale
em3ry said:
I know that. I am asking for the classical explanation.

Water waves would pass through an obstruction like that. Why don't electromagnetic waves?
The classical explanation is that if we setup a conducting grid like that of a microwave door and apply Maxwell's equations on that grid with an incident plane EM wave, then the percentage of the plane EM-wave energy that passes through is proportional to the ratio ##\frac{d}{\lambda}## where ##d## the spacing of the grid and ##\lambda## the wavelength of the incident plane EM wave. So there is not an absolute shielding if that was your main concern(unless we make ##d=0##, hence a solid plate and not a grid), there is always some percentage that passes through, it is just that this percentage is really small if the wavelength is big in comparison to d.

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dRic2, tech99, lomidrevo and 1 other person
em3ry said:
I know that. I am asking for the classical explanation.

Water waves would pass through an obstruction like that. Why don't electromagnetic waves?
What frequency do you suppose that water waves, which are not EMR waves, might have? Sound waves also are non-attenuated by a Faraday cage. I think that the explanation provided by @Halc is 'classical' and spot-on correct.

Halc and Delta2
As to why water or sound waves pass through a grid but not EM waves, i believe it is because the interaction of water waves with a grid is described by Navier-Stokes equations while we have Maxwell's equations on the other case.

dRic2 and sysprog
Halc said:
A classical explanation of a quantum effect is like asking for an explanation of chemistry in terms of air, water, Earth and fire.
But if it pleases you, envision the photons as particles that don't fit through the holes if they're too big.
Photons have no definite size nor a position. I don't know for what you need a quantum description of a microwave oven, but a photon in this case is a Fock state of a cavity mode. The probability to detect a photon is given by the (time-averaged) energy density of the field mode and that's just constant, i.e., in this sense a photon fills the entire cavity.

sysprog and tech99
Boy, did this get off on the wrong foot!

It is not true that photons or quantum mechanics is required to understand this. It's purely classical.

It's also not true that water waves do not experience similar phenomena. If you set up the same boundary conditions you will get the same sort of effect. Setting that up (wave amplitude zeroes at regular intervals) is a bit of a trick, of course. You don't simply dip a screen window in an ocean.

dRic2, Dale, em3ry and 2 others
It's also not true that water waves do not experience similar phenomena. If you set up the same boundary conditions you will get the same sort of effect. Setting that up (wave amplitude zeroes at regular intervals) is a bit of a trick, of course. You don't simply dip a screen window in an ocean.
I have the door shielding from an old microwave and I have some water. (I never throw anything out. I actually kept it for the magnet.)

em3ry said:
What is the classical explanation for why the microwaves won't pass through the microwave door?
There are a number of ways of explaining this action.

If the hole is considered to be a short tube, then we can notice that it is a metal waveguide. For energy to propagate through a tube, the diameter needs to be roughly half a wavelength or the wave cannot fit in the tube and we say the waveguide is cut-off. So a hole which is only a small fraction of a wavelength will not propagate energy very well.

Alternatively, we can notice that a continuous sheet of metal will act as a reflector because the incident electric field encounters a low resistance across the surface, which effectively short circuits it and causes zero energy to be absorbed by the surface and the wave to be reflected. The holes in the surface introduce only a small increase in surface impedance, provided they are small compared to the wavelength. If, however, they are about half a wavelength diameter they approach resonance and introduce a high surface impedance which allows the incident electric field to pass unhindered.

To help understand the surface impedance idea, we can consider a glass window with small patches of metal on it. This is the opposite of the metal sheet with holes - we call it the complement under Babinet's Principle. The small patches do little to reflect the radiation because, being only a small fraction of a wavelength in size they have a high capacitive reactance and so carry very little current. The holes, by contrast, are the complement and have a very low inductive reactance, so carry large current, nearly the same as the uninterrupted sheet.

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Halc said:
But if it pleases you, envision the photons as particles that don't fit through the holes if they're too big.
You have fallen into the trap of assuming that introducing photons into an explanation gives depth to it and gives better understanding. In fact, it's quite the reverse. This and many other phenomena are far better described in terms of waves. If you want to talk about the 'size' of a photon then you are on extremely shaky ground. How would you go about doing that? The idea actually has no meaning because the photon has no mass and time means nothing to an entity that travels at c. . You have come across Young's slits, I assume. In that experiment, the energy of a photon goes through both slits and the phenomenon works, however wide the slits are spaced. There are practicalities involved, which limit the actual probability of energy actually getting through because the probability is a lot greater that the plate will intercept the energy but that photon has to be regarded as possibly being all over the plate (and possibly being anywhere in space).

davenn, nasu, vanhees71 and 2 others
sophiecentaur said:
You have fallen into the trap of assuming that introducing photons into an explanation gives depth to it and gives better understanding.
Oh I realized that. Here I was trying to dumb down an explanation to the point of making it wrong, and I go and introduce a photon, a quantum thing that was the very thing from which I was trying to distance my reply.

Halc said:
Oh I realized that. Here I was trying to dumb down an explanation to the point of making it wrong, and I go and introduce a photon, a quantum thing that was the very thing from which I was trying to distance my reply.
Teaching via the negative can be very confusing unless you are dealing with a very simple system - say the Young's Slits.

The explanation of how holes in a metal plate affect an EM (!) Wave is difficult. Why use that as an excuse to bring in photons?

vanhees71
Delta2 said:
So there is not an absolute shielding ...
As can be demonstrated by calling a cell phone placed in a closed microwave oven. It will often work, depending on the oven, cell phone type and signal strength in the apartment.

vanhees71 and Delta2
em3ry said:
I know that. I am asking for the classical explanation.

Water waves would pass through an obstruction like that. Why don't electromagnetic waves?
How is not Halc's explanation "classical"? Diffraction and Faraday cage where known well before qm and sr.

Of course this is all classical electrodynamics which is a classical field theory (i.e., not QM, but it's relativistic). I don't know, why people always bring up photons when they have a completely classical electromagnetic problem. Photons are unnecessary in such cases and the calculations are pretty much the same anyway ;-)). Almost always you cannot treat photons as particles! If you can, it's a problem solvable with geometrical optics (eikonal approximation of Maxwell's equations), but this doesn't apply for questions involving diffraction.

dRic2 and sysprog
Halc said:
The grate in the window acts a sort of a Faraday cage preventing radiation from passing through. The wavelength of the microwaves need to be at least twice the the hole diameter for it to work properly.
2450 MegaHertz magnetron frequency of microvave ovens has a wavelenght of 10 centimeters. From microscopy there was a optical limit of detection being half a wavelength, the holes in my microwave door grating are ~1mm.

vanhees71 and Keith_McClary
shjacks45 said:
2450 MegaHertz magnetron frequency of microvave ovens has a wavelenght of 10 centimeters. From microscopy there was a optical limit of detection being half a wavelength, the holes in my microwave door grating are ~1mm.
The limit of half a wavelength is just a practical guide, as there are now microscopes able to see smaller objects. A similar effect occurs with a radio antenna, where half a wavelength is a practical limit but in theory there is no smallest size which can radiate or receive energy. The very small structures have electrical reactance which reduces the flow of curent, but in theory this can be balanced out by adding inductance or capacitance (in practice, resistive losses soon make this impractical). Looking at the microwave screen, the holes have a small inductive impedance which does not hamper the flow of surface current. If, however, a capacitor was connected across the hole, so that it was resonant, its impedance would become very high. This would reduce the surface current and allow radiation to pass throuigh the screen.