PHYS-302, Physics of Waves (Summer 2007)

M9 - EM Waves in Conductors (and Fun with Microwaves) (Chapter 9 with supplements)

Topical Outline for two-hour class:

Wave Equation in Conducting Medium - we reviewed the modified wave equation for EM waves in a material and discussed the case where the medium has a finite conductivity.
Skin Depth - we determined the skin depth (distance EM waves penetrate into a conducting material).
Model of Conductivity - we looked at a simple model of conductivity and used it to estimate the frequency of electron collisions with the atoms in the conductor. EM waves with frequencies below this "collision frequency" will propagate in the conductor but will be severely attenuated (amplitude decays exponentially over a very short distance).
Plasma Frequency - we used the simple model of conductivity to expore the complex wavenumber for wave propagation in a conductor and arrived at a dispersion relation that we had encountered earlier in the term, when we looked at waves in a waveguide. EM waves with a frequency below the plasma frequency cannot propagate in the metal (evanescent decay) and are completely reflected from the metal surface. EM waves with a frequency above the plasma frequency can propagate in the conducting material, and the material becomes "transparent" to the EM waves.
Hands-on Activity - Fun Experiments with Microwaves

Hands-on Activities

Frequency of Microwaves

We wanted to answer the question of whether or not microwave ovens are safe - whether or not microwaves can penetrate the metal screen mesh embedded in the glass window and "radiate" the user. We obtained an estimate of the frequency by measuring the wavelength for standing EM waves inside the microwave oven. We first tried to use a tray of closely packed marshmallows expecting to find burn marks at the antinode locations after running the oven for several minutes. But, we used large marshmallows instead of mini ones, and the large marshmallows expanded too much and started burning on the inside instead of on the outside. So, we couldn't find the antinodes of the EM standing wave. We ate them (tasted good), and then repeated the experiment the next day using chocolate chips. Covering a tray with chocolate chips and running the microwave for just over a minute, we were able to clearly find some "hot spots" where the chips were beginning to melt. This was a tasty experiment (next time we'll have to bring some graham crackers to make S'mores!)

As shown in the photos below, we measured an average distance between antinodes (melted regions) of about 6 cm, which results in a wavelength of approximately 12 cm, and a frequency of about 2.5 GHz. This agrees pretty well with the fact that most modern commercial microwave ovens operate at about 2.45 GHz. This wavelength is 100 times larger than the size of the holes in the screen mesh in the window, so that the mesh appears to be a solid wall as far as the microwaves are concerned. Also, the operating frequeny of 2.5GHz is several orders of magnitude below the plasma frequency for most metals, so that the microwaves cannot penetrate into the metal screen mesh and are completely reflected by the metal mesh and the metal walls enclosing the cooking area of the oven.

Powering a Flourescent Light Bulb with Microwaves
According to one of the reference texts for this class [Electromagnetic Vibrations, Waves and Radiation by George Bekefi and Alan H. Barrett (MIT Press, 1977)] the gas in most flourescent light bulbs has a plasma frequency around 2.9GHz, which is pretty close to the operating frequency of our microwave oven. This suggests that we should be able to make a flourescent bulb glow (without plugging it in) simply by exposing it to EM radiation with the right frequency.

The microwave we used (a 1986 model that Dr. Russell's parents owned when he was an undergraduate student) was large enough to place a 15" flourescent tube completely inside. We covered the metal terminals with electrical tape to prevent arcing, placed the bulb inside and turned on the microwave for 10 seconds. After a about a second, the bulb flickered and began glowing - and it glowed brighter than it would have if normally plugged into to an AC socket.

Important Safety Concerns:

covering the terminals with electral tape is necessary to prevent arcing which can damage the microwave oven.
running the microwave longer than 10 seconds can cause the flourescent bulb to melt.
The reason that a microwave heats food is that the dipole nature of water molecules causes the water molecules to rotate in response to the alternating electric fields, with a significant amount of damping so that the kinetic energy of the water molecules is convered to heat. If there is no moisture in the oven while running, the standing EM waves in the oven can become very large and can damage the oven. Placing a cup of water in a corner of the oven allows the microwave energy to be absorbed (heating the water) and prevent dangerous buildup of standing waves.

15" flourescent bulb in the microwave (cup of water is to provide absorprion for the EM standing waves).

The flourescent bulb is beginning to glow.

The flourescent bulb is glowing more brightly than it normally would when connected to an electrical lamp fixture.

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