# Physics of microwave oven

I am looking for a definitive discussion of the physics of microwave oven - I mean I would like to see actual evidence in favor of this or that explanation, rather than just popular physics/schoolteacher type of answers (as is the case in many answers dealing with microwave ovens in this SE, my own included - but I haven't done an exhaustive search.)

The immediate questions that come to mind:

• How exactly is food heated? Do microwaves penetrate all the way inside or do they heat only the surface layer?
• Why soup takes longer to heat? Because of water transparency to microwave and low heat transfer or because of higher heat capacity?
• Why it is better not to place food in the center of the rotating plate, but rather let it perform a circular trajectory with the turn-table - because of the nodes of the standing wave, despite the highly irregular form of the object inside the microwave?
• This veritasium video isn't about how microwave ovens work in general. But it does have some interesting physics. Microwaving Grapes Makes Plasma. Another thing you can do is put carbon fibers in a microwave. They of course immediately burn. But if you put them in an evacuated test tube. They glow like a light bulb. I imagine steel wool would work, but I haven't tried it. Commented Apr 15 at 15:32
• "water transparency to microwave" The point of microwave ovens is to heat water. i.e. Water is most opaque to microwaves. Only the surface layer from any non-metallic container edge would be heated, so your front two questions would be answered immediately. Commented Apr 15 at 16:14
• sfu.ca/phys/346/121/resources/physics_of_microwave_ovens.pdf Commented Apr 15 at 19:42
• @mmesser314, if you heat steel wool to "like a light bulb" temperature, it will melt. Commented Apr 15 at 22:23

How exactly is food heated? Do microwaves penetrate all the way inside or do they heat only the surface layer?

This is a complex problem because the penetration depth, intensity to drop by 1/e, depends on the frequency, relative permittivity and conductivity as $$D=\frac{0.225 \lambda}{\sqrt{\epsilon_r}\sqrt{\sqrt{1+\tan^2\delta}-1}}$$ where $$\tan \delta =\frac{\sigma}{\epsilon_r\epsilon_0}.$$ The absorbed power is $$P=\sigma |E_i|^2$$ but the intensity in the food $$E_i$$ is a complicated function of the illumination and material properties. Even heating a cup of water results in a nonuniform heating that only equalizes by stirring or conduction because the field penetrating the water is not uniform due to these losses. The more complex the food is in its $$\epsilon$$ and $$\sigma$$ the less its uniformity as the field penetrates. The 915MHz oven of days of old was just as prone to uneven heating as the newer 2.45GHz one despite its 2.6$$\times$$ longer wavelength.

Why soup takes longer to heat? Because of water transparency to microwave and low heat transfer or because of higher heat capacity?

Water has high permittivity (smaller penetration length) and high heat capacity, both would imply longer heating time.

Why it is better not to place food in the center of the rotating plate, but rather let it perform a circular trajectory with the turn-table - because of the nodes of the standing wave, despite the highly irregular form of the object inside the microwave?

The design of the cavity dimensions aims to maximize the number of modes that can simultaneously exist in the band $$2450\pm50\rm{MHz}.$$ More standing waves, modes, the more uniform is the field within the cavity. Unfortunately, the presence of the food (life is hard sometimes) with its varying, rather unpredictable properties, detunes this theoretical arrangement and nodes or low intensity locations may develop. To make it more uniform, in addition to the rather common rotating glass table holding the food, in the waveguide that illuminates the cavity a rotating wave "disperser" is sometimes placed. These unpredictable mode structures that develop has another rather unfortunate effect, namely the increasing reflection back to magnetron can both detune it and lower its output power. I have not heard that any commercial oven would be using an isolator to overcome this problem, probably because of the prohibitive costs of a 1kW/2.5GHz isolator with its additional weight and size. The glass plate holder, be it rotating or not, is needed to have some absorber if the user were to forget to load the cavity; otherwise the tube might blow up from all the reflections.

In a theoretical analysis of a typical domestic microwave oven cavity with dimensions $$342(W) \times 195(H) \times 357(D) \rm{mm}^3$$ and the turntable diameter about 325mm, the cavity had 108(!)modes and despite of that the field was still fluctuating 30dB at $$100\rm{mm}$$ above the bottom! When rotating it most points will fluctuate about $$\pm3\rm{dB}$$ but not within ~10mm of the center where it can still have 10dB variation according to the simulation.

• i deleted my answer- yours is far better. -NN Commented Apr 16 at 16:23

I'm going to do a schoolteacher type answer anyway, sorry, but I like doing things in the simplest possible terms:

How exactly is food heated? Do microwaves penetrate all the way inside or do they heat only the surface layer?

Microwaves operate at a frequency that resonates with water molecules. Other frequencies pass through water molecules, but the right microwave frequency transfers lots of its energy to heating H2O. (pro tip: if you're heating up something dry like cookies or hot dog buns, drip a little water on them first)

Why soup takes longer to heat? Because of water transparency to microwave and low heat transfer or because of higher heat capacity?

Really just the higher heat capacity. Try heating soup in an oven.

Why it is better not to place food in the center of the rotating plate, but rather let it perform a circular trajectory with the turn-table - because of the nodes of the standing wave, despite the highly irregular form of the object inside the microwave?

Yup, that's pretty much all there is to it. You can put a long stick of butter in a microwave to see where the nodes/antinodes are.

One additional factor is that for a given volume of material/water, stuff near the surface dissipates heat to the air whereas heat in the center is trapped. So it's good to move things around to heat more evenly.

• The frequencies 915MHz (very old ovens) and 2450MHz (all ovens since the 60s) have nothing to do with any molecular or atomic transition resonances. Litton had magnetrons around the lower L-band <1GHz and Raytheon had them in the S-band ~2-3GHz after WWII when they had to do something with their magnetron technology. The 915MHz went out fashion not because it could not heat water as well the other but because the cavity, the magnetron and all its surrounding electronics had to be 2.5x bigger and heavier and more expensive, what remained is the 2450 ISM frequency allocation, Raytheon won. Commented Apr 16 at 12:14