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I am familiar with the concept that electrical fields within a Faraday cage do not extend outside of the cage and that electrical fields generated outside do not extend into it.

My question is -- when an electrical face is generated inside a Faraday cage (say as in a microwave) does the cage act as a reflective surface to amplify the field? If so, how is this calculated for different types of material (say nickel vs iron)? Does the efficiency of this reflection decrease with increasing fields?

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  • $\begingroup$ what is an electrical face? $\endgroup$
    – Bob D
    Nov 5 '21 at 21:24
  • $\begingroup$ typo, *electrical field $\endgroup$
    – plumpy
    Nov 5 '21 at 21:37
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The "cage" acts as reflector of EM waves, but I am not sure it is good to call this "amplifying". It just reflects the waves that are generated inside, it does not boost their amplitude. Reflection from metallic walls is close to 100% for low enough frequencies (microwave oven usually works at 2.4 GHz which is well in this range), but the higher the frequency, the worse the reflection is, and the more energy gets dissipated in the metallic walls. For X-rays or higher frequency radiation, not even metallic sheets would work as good reflectors. Different metals will differ slightly in reflection properties (because of different composition, they have different absorption spectrum).

In a real microwave oven, there is a cavity for the meal, but this cavity is not exactly the simple Faraday cage, as it has an opening through which EM radiation from magnetron comes in. Magnetotron is generator of EM waves using rotating parts and strong voltages and currents. So the EM waves are actually generated outside the imperfect "Faraday cage" and then let inside through the opening. The walls of the cage just help the radiation concentrate near the meal, but they do not actively increase its intensity.

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The reflective walls of a microwave cavity do indeed increase the intensity of the microwave radiation being beamed into it, simply by leaving it no path to escape. For the case of an empty microwave oven, the radiation density in the cavity climbs and climbs as the magnetron runs and eventually gets so high that it will back up into the feedhorn and wreck the magnetron. This is why you are advised against running a microwave oven with nothing inside it.

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  • $\begingroup$ Is there a mathematical equation that describes the degree of reflectiveness? For example, something taking into account atomic weight/thickness of the cage and energy of the radiation? (like say the walls of a microwave were solid metal instead of a mesh or lead instead of aluminum, how much faster would it heat an object etc.) I would assume these have to be published somewhere for industry safety standards with shielded devices. $\endgroup$
    – plumpy
    Nov 6 '21 at 13:01
  • $\begingroup$ @plumpy, the equations are big & messy but the single most important thing is the electrical conductivity of the walls. High conductivity means almost perfect reflection and then the buildup of energy in the cavity is linear with time, up to the point where the feedhorn gets choked and the magnetron begins to crap out. The other important factor is the size of the perforations in the oven door. for near-perfect reflection you want the holes to be no bigger than ~1/100th the wavelength of the microwave beam. $\endgroup$ Nov 6 '21 at 18:12

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