# Why metals spark in microwave ovens?

Hi, sorry for the childish title. But this problem is supposed to be solved quantitatively using Laplace's equation, so it's not so straightforward.

## Homework Statement

(a) Explain why it is possible to keep a teaspoon in a cup of water heated in a microwave oven without spark formation, but if you place a piece of aluminium foil in the same microwave oven, you will see sparks.

(b) For a quantitative description, it is useful to calculate the electrical fields at the tip of a conductive wedge held at a potential V0 by solving the Laplace equation for this geometry.

## Homework Equations

$\nabla$2V=0

## The Attempt at a Solution

In a microwave oven, the electromagnetic waves are tuned to coincide with the resonant frequency of water molecules. Hence, there is maximum transfer of energy from into the water, which gradually boils off as it dissipates the incident electromagnetic energy away into thermal energy. A metal teaspoon in the water is effectively shielded from exposure to the microwaves and thus does not acquire the energy requisite to spark formation.

For a free aluminium foil, the situation is very different. Electromagnetic micro waves pass through food, plastic and glass, but reflect off metal. The electrons on the surface of the metal will jump off of the metal object and into the air, which causes a spark in the microwave oven.

Another critical factor is the existence of numerous pointed, sharp edges on a foil; the local electric field at a sharp edge may be strong enough to ionize the adjacent air and cause an electric discharge through it. Whilst the current is passing through the air, various electronic transitions may occur in the visible electromagnetic spectrum which manifests in the form of sparks.

(b) I really need help for this part. Currently I am using the Griffiths’ Intro. To Electrodynamics book at university, and have completed Chapter 3 on solving Laplace’s equation in Cartesian, spherical and cylindrical coordinates. However I genuinely can’t see how all these things can help to find the e-field of a conductive wedge in a microwave oven!
My assignment is due on Friday, so any prompt help is greatly appreciated.

Thanks so much.

Related Advanced Physics Homework Help News on Phys.org
fluidistic
Gold Member
From http://paul-a-heckert.suite101.com/why-no-metal-in-microwave-ovens-a35382,
Thin wires have more electrical resistance than thick wires, so a thin wire will heat up more than a thick one, if it carries an electric current. Thin metal objects inside a microwave oven can therefore get very hot from these electric currents.
, it seems to be the reason why the walls of the microwave oven don't spark despite being metallic.

Your comment "In a microwave oven, the electromagnetic waves are tuned to coincide with the resonant frequency of water molecules" is incorrect. The resonant frequency of water at room temperature is approximately 22 GHz, while the microwave oven frequency is 2.45 GHz. This results in two phenomena:
1. Water is predominantly (~60%) a reflector, but because the waves pass thru the water multiple times, the energy transfer "adds up" and the water heats well.
2. As water becomes hotter, its resonant frequency increases, while the oven frequency remains the same - this results in water heating at a slower rate as it becomes hotter.
The oven frequency of 2,45 GHz was chosen partly because of the availability of magnetrons at the frequency. Also, the penetration depth is reasonable (~1.3 cm), while it would be so small at 22 GHz as to be more like surface heating

fluidistic
Gold Member
Being in front of a microwave oven guru, I really want you to ask a question that boggles me (I don't want to go too off topic so you can PM me if you don't want to hijack here).
Ice can be considered mostly as a black body for any EM wave outside of the visible spectrum. It means it should absorb very to extremely well microwaves (so that they cannot penetrate really deep inside the ice). Then why is it so hard to melt ice into water in a microwave oven?

Remember that water heats because it is an electrical dipole and is constantly vibrating. This vibration is affected by the presence of the rapidly oscillating microwave (electrical) field and this causes the heating. However, ice is frozen water in which water molecules are caught in a crystalline lattice and are not free to rotate, so they are not affected by the microwave field. At ordinary freezing temperatures there is still some free water, so ice is not totally transparent to the microwaves - you probably have to go below minus 100C in order to reduce free water to zero or close to it.
Another fascinating thing is that cold water heats faster in a microwave oven than warm water - try it with 10C, 20C & 30C water - exactly the same amount (say one liter), for exactly the same time (say 60 seconds). At 10C the resonant frequency of water is closer to 2.45 GHz.

fluidistic
Gold Member
However, ice is frozen water in which water molecules are caught in a crystalline lattice and are not free to rotate, so they are not affected by the microwave field. At ordinary freezing temperatures there is still some free water, so ice is not totally transparent to the microwaves - you probably have to go below minus 100C in order to reduce free water to zero or close to it.
So basically ice below -100°C does not behave like a black body nor a white body (i.e. it doesn't reflect the microwaves either), it just let the waves pass through itself with very few interaction, hence no heating or almost no heating. However if the ice is close to 0°C the few water that is on its surface will be the reason of the -slow- heating of ice into water.

But I still wonder why then the emissivity of ice is so close to 1 for micro waves. Wouldn't this mean that it should also absorb these wavelengths? Instead of just let the waves pass through it.

Interesting question and I can only speculate on the answer. Note that there is little difference between the emissivity of ice & water; this is possibly due to there always being a monomolecular layer of water on the surface of ice until the temperature drops to minus 100C or less (that's why ice skates glide so well on ice). Since this layer is so thin it can't capture enough microwave energy whose free-space wavelength is 12.2 cm, and whose wavelength in water is on the order of 1.3 cm. So the microwaves are free to travel thru the ice after having past the surface.

Sorry for interrupting this thread :)
I am looking for simple explanation about why metals spark in microwave ovens. I never knew about this before until I came across with one video in youtube. Can anyone helps explain this phenomenon to me in a simplest way.

Sparks (arcs) are caused by electrical breakdown (ionization) of the air. That take a field strength of about 33 Kvolts/cm in air at standard temperature & pressure. This threshold reduces as pressure decreases, which is why microwave energy has never been successfully used for freeze-drying coffee. In order for there to be an arc, you need something else - a gap between two metal points or edges, and the gap distance is important - if the gap is 1 cm, you need approximately 33 Kvolts; reduce that and the breakdown voltage decreases proportionally. It is similar to the carbon arc lamps used for projecting movie films for years - you caused a current to flow in one carbon rod - the other is held at ground ... bring the two rods close together and an arc forms in the gap, and "there is light!

In order for there to be an arc, you need something else - a gap between two metal points or edges, and the gap distance is important - if the gap is 1 cm, you need approximately 33 Kvolts; reduce that and the breakdown voltage decreases proportionally.
So, it is the same as arc welding right? Gap is needed so that electron can jump to the workpiece in the form of arc. Which one is more accurate? electron or metal ion that jump to the workpiece?

Ok back to my original question about microwave. I am not really understand about the gap. Let say, I put metal rod inside the oven. Can you explain to me which one is the gap that you are referring to?

Sorry to ask childish question :). Sometimes I am a slow learner and need more clarification so that I can understand something. Sorry again to trouble you :)

The gap is important because you need a high electrical potential - large enough to cause the voltage to "jump the gap" and that is 33 kv/cm - that's a very large voltage - if the gap is larger, the voltage has to be proportionally larger; if the gap is smaller the voltage is proportionally smaller. In a microwave oven my experience is that a 1 cm gap is too large because the electric strength (the voltage) is not high enough. But if you reduce the gap to 1 mm the required field strength to cause the breakdown arc drops to 10 %, about 3000 volts, and you are likely to get an arc.

As to your question of a rod - the two ends are far apart; also, the current flows thru the rod. If you put a second rod so that its tip is close to the first, you may get an arc.

Your comment "In a microwave oven, the electromagnetic waves are tuned to coincide with the resonant frequency of water molecules" is incorrect. The resonant frequency of water at room temperature is approximately 22 GHz, while the microwave oven frequency is 2.45 GHz. This results in two phenomena:
1. Water is predominantly (~60%) a reflector, but because the waves pass thru the water multiple times, the energy transfer "adds up" and the water heats well.
2. As water becomes hotter, its resonant frequency increases, while the oven frequency remains the same - this results in water heating at a slower rate as it becomes hotter.
The oven frequency of 2,45 GHz was chosen partly because of the availability of magnetrons at the frequency. Also, the penetration depth is reasonable (~1.3 cm), while it would be so small at 22 GHz as to be more like surface heating
Remember that water heats because it is an electrical dipole and is constantly vibrating. This vibration is affected by the presence of the rapidly oscillating microwave (electrical) field and this causes the heating. However, ice is frozen water in which water molecules are caught in a crystalline lattice and are not free to rotate, so they are not affected by the microwave field. At ordinary freezing temperatures there is still some free water, so ice is not totally transparent to the microwaves - you probably have to go below minus 100C in order to reduce free water to zero or close to it.
Another fascinating thing is that cold water heats faster in a microwave oven than warm water - try it with 10C, 20C & 30C water - exactly the same amount (say one liter), for exactly the same time (say 60 seconds). At 10C the resonant frequency of water is closer to 2.45 GHz.
The resonant frequency of water at 10C is ~ 2.45GHz and at room temperature which is about 20C its ~22GHz. A difference in half the temperature is equivalent to an order of magnitude in the frequency. Is this a linear correlation? ie is the resonant frequency at 0C ~.2GHz?

As to your question of a rod - the two ends are far apart; also, the current flows thru the rod. If you put a second rod so that its tip is close to the first, you may get an arc.
So, I can conclude, in order to successfully produce spark in the oven, I need at least two metal rod which are closer to each other right?
Is there any other criteria or metal properties that I need to take into account? Actually, I was wandering whether every metal can produced the same amount of energy (spark) or the energy depend on the conductivity of the metals and their permeability.

Yes - the metal rods have to have good electrical conductivity and this can vary in different metals. Interestingly, carbon particles also arc to each other

Yes - the metal rods have to have good electrical conductivity and this can vary in different metals. Interestingly, carbon particles also arc to each other
Do you know the equation that can relate the energy produce by the spark with metal conductivity?

No, you'll have to search the literature

Last night I put small copper rod into microwave. It did not spark. Why it did not spark?

fluidistic
Gold Member
Last night I put small copper rod into microwave. It did not spark. Why it did not spark?
yourself said:
So, I can conclude, in order to successfully produce spark in the oven, I need at least two metal rod which are closer to each other right?

The resonant frequency of water at 10C is ~ 2.45GHz and at room temperature which is about 20C its ~22GHz. A difference in half the temperature is equivalent to an order of magnitude in the frequency. Is this a linear correlation? ie is the resonant frequency at 0C ~.2GHz?
No, the resonant frequency is about 10 GHz @ 10 C; there is a relationship and given by Debye 1929 Polar Molecules, Chemical Catalogue New York. You can see a graph in Table 2.7 in Metaxas: " Foundations of Electroheat: A Unified Approach" published by John Wiley