Suppose one has a 1000 watt microwave oven operating at 2450 MHz or a
0.122 meter wavelength. We introduce an 18-gage (one-mm diameter)
tightly wound wire coil composed of 40 one-millimeter diameter turns
connected end to end in order to complete the circuit. We turn the
microwave oven on. Will there be an induced current in the coil? If
there is, then suppose it is 13 milliamps. The resistance of the wire
is about 0.034 ohms per meter (according to my reference) so the heat
of the coil would be 0.034x0.122x (0.013) squared = 7 times ten to the
minus seven watts. Suppose that I fill the oven with 1.4 times ten to
the ninth such coils for a total heat of 1000 watts and turn the oven
on. Will the coils absorb this microwave-oven power and induce the 18
milliwatt current in each coil?

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Clarification of Question by drbaker-ga on 14 Nov 2003 06:55 PST

If the coils will respond to the microwave oven field by circulating
an induced current, then very approximately (assuming some fractional
power loss or uneveness in the field) what would the current be in the
1.4 times ten to the ninth coils heated up in the 1000-watt rated
microwave oven? (Apparently not 18mW.)

Really Dr Baker!

     What a strange experiment - packing over e9 coils into one
ordinary microwave! If you want to bake that many coils,
 I would recommend industrial conveyor belt oven, like this
www.doyon.qc.ca/service/en/fc16e.pdf

	That's because microwave rated at 1000W will not necessary
 consume 1000W. If it is empty, it will consume less, since impedance
 is high. If it is bursting with conductive coils, it may try to deliver more
 and possibly burn the magnetron tube or blow a fuse.
        Then you assume current will be 13 milliamp and ask if it will be
18 mW (milliWatts?) which I suppose is a type fro 18mA ?
Answer to that would be 'no'. It would be 13 mA.

    Seriously: if you could pack a really well designed micro wit that
many coils, and it would limit the imput power to 1000W, then each coil
would have about equal share of power, that is 1000 /(1.4E9) = about .7 mW,
less then milliwat. Metal coil may have a problem with that input, since
metal has higher conductivity (both electrical and thermal) than water -
so I would caution you that such experiment my void warranty and induce
ire in the local fire marshal.
     Finally, what curretnt would flow in the wire cannot be determined
since to know resistance is not enough.
 You would have to also estimate inductance of the coils to calculate
the current from the power consumed. The formulaes do exist, and for
air core it would depend mostly on the inner radius of the coil, which
was not given.
Formule for coils Inductance are here
http://www.epanorama.net/wwwboard/messages/5607.html
and heating etc is debated here
http://www.fnrf.science.cmu.ac.th/theory/magnets/An introduction to
the air cored coil.html

Search Terms
Air core coils, inductance
How microwave works 

 e.g.  By adjusting the on-off ratio of this activation signal, the
control system can govern the application of voltage to the
high-voltage transformer, thereby controlling the on-off ratio of the
magnetron tube and therefore the output power of the microwave oven.
Some models use a fast-acting power-control relay in the high-voltage
circuit to control the output power.
http://home.howstuffworks.com/framed.htm?parent=microwave.htm&url=http://www.gallawa.com/microtech/how_work.html

and
impedance, parallel circuit 
e.g.
http://www.ecmweb.com/ar/electric_basics_seriesparallel_circuits/
 (your coils are all in prallel, sharing the power equally).

  I hope the analysis was useful, that these are all thought experiments
 and that you do not mind few prickly and impertinent comments in the answer.
 What else could you expect from a

hedgie

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Clarification of Answer by hedgie-ga on 15 Nov 2003 06:49 PST

errata:

instead of

http://www.fnrf.science.cmu.ac.th/theory/magnets/An introduction to
the air cored coil.html

(all one URL with 91 characters)

try  this 
http://tinyurl.com/v4ar

it expands to the same name long, which has illegal URL syntaxs and so
gets malformed in text.

The short form should work and really is the webdesigners error.

You inquired as to what I was up to. You can determine that from my
web page: www.drrobertbaker.com or from www.gravwave.com. Simply put:
I am designing a high-frequency gravitational wave (HFGW) generator.
The basic equation (the quadrupole published by Einstein in 1916) to
determine the HFGW power when modified is: 1.76 times ten to the -52
times the quantity: twice the radius of gyration (m) of an array of
masses times a change in force (N)on them divided by the time (s) to
achieve that force change, squared (power in watts). The concept is to
situate the masses along a ring, jerk them (delta force divided by
delta time) tangentially and then detect the HFGW along the axis of
the ring. If the pulses are in a continuous train then the jerk is
delta force times the frequency of the train, hence the need for high
frequency. I have been casting about (often with your help) for
devices to achieve very short duration force pulses (the shorter the
better – femtosecond and attosecond – THZ and PHz are good). I have
looked at energizing/energizable elements consisting of air-core coils
surrounding a permanent magnet mass, photons “banging” back and forth
in a laser, etc. with the objective to obtain large jerks and also to
find a means to power the energizing elements. I am still searching.
Thanks for you help. Bob Baker

very interesting! well... the answer is yes the coil will induce the
electromagnetic energy BUT i dont think the 18mW will be generated in
a series coil circuit because you can attract/absorb more of
electromagnetic energy in seperate coils.if you use a series coil
circuit some of the electromagnetic enrgy will be lost therefore
1000watts will not be absorbed resulting in energy loss

I would like a clarification to my question. If the coils will respond
to the microwave oven field by circulating an induced current, then
very approximately (assuming some average fractional power loss
throughout the oven)what would the current be in each of the 1.4 times
ten to the ninth coils heated up in the 1000watt rated microwave oven?
(Apparently not 18mW.)