Microwaves

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Microwaves

• Physics of Modern Devices
• February 23, 2009

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Electromagnetic Waves

• Last week we learned that EM waves can carry
  sound from one place to the other
• Example Radio
• EM waves can also carry power
• Example Microwave oven
• High frequency EM waves to transfer power
  directly to the water molecules in food

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More on Electromagnetic Waves

• The wave equation for a plane electric wave
  traveling in the x direction in space is
• with the same form applying to the magnetic field
  wave in a plane perpendicular the electric field.
  
• Both the electric field and the magnetic field
  are perpendicular to the direction of travel x.
• The wave equation for electromagnetic waves
  arises from Maxwell's equations.

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More on Electromagnetic Waves

• The form of a plane wave solution for the
  electric field is
• and that for the magnetic field
• To be consistent with Maxwell's equations, these
  solutions must be related by
• The magnetic field B is perpendicular to the
  electric field E in the orientation where the
  vector product ExB is in the direction of the
  propagation of the wave.

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Maxwells equations

• Gauss' law for electricity
• Gauss' law for magnetism
• Faraday's law of induction
• Ampere's law

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Microwaves

• Today we will address these questions about
  microwaves
• Microwave ovens cook food from inside out
• They can cook foods unevenly
• They dont defrost foods well
• You shouldnt put metal inside them?!

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Electromagnetic Spectrum

• Long-wavelength EM waves Radio Microwave
• Wavelengths longer than 1m
• AM Radio 545 m - 187 m
• FM Radio 3.4 m - 2.8 m
• Wavelengths shorter than 1m
• Microwaves 1m - 1mm (3.3ft - 0.04in)

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More on Microwaves

• Microwaves are radio waves.
• In the case of microwave ovens, the commonly used
  radio wave frequency is roughly 2,500 MHz (2.5
  GHz).
• Radio waves in this frequency range have an
  interesting property they are absorbed by water,
  fats and sugars.
• When they are absorbed they are converted
  directly into atomic motion -- heat.
• Microwaves in this frequency range have another
  interesting property they are not absorbed by
  most plastics, glass or ceramics.
• Metal reflects microwaves, which is why metal
  pans do not work well in a microwave oven.

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Water Molecules

• Water molecules are electrically polarized.
• Positively charged and negatively charged ends
• Why?
• Quantum physics and the tendency of oxygen atoms
  to pull electrons away from hydrogen atoms
• When oxygen atom pulls the electrons partly away
  from hydrogen atoms, its side becomes negatively
  charged while hydrogen side becomes positively
  charged

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Hydrogen bond

• In ice, polar water molecules are arranged in
  orderly fashion with fixed positions and
  orientations.
• In liquid water, the molecules are randomly
  oriented
• Their arrangements are constrained by their
  tendency to bind together
• Binding between positively charged H atom on one
  molecule with negatively charged O atom on other
  molecule
• Hydrogen bond
• Explains many of the properties of water
• Relatively high melting and boiling point
  temperatures more heat energy is required to
  break the hydrogen bonds between molecules.
• Ice has lower density than liquid water expands
  as it freezes molecules rearranged to minimize
  energy.

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Water Molecules, cont

• Water molecules are unusually polar
• An electric field orients water molecules
• A fluctuating electric field causes water
  molecules to fluctuate in orientation
• A misaligned molecule will undergo an angular
  acceleration that makes it rotate into alignment
• As it rotates, the molecule will bump into other
  molecules and convert some of its electrostatic
  potential energy to thermal energy
• If E field reverses its direction many times, the
  water molecules will turn back and forth and
  become hotter and hotter

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Microwave Heating

• Microwaves have fluctuating electric fields
• 2.5GHz
• Frequency chosen since it is not in use for
  communications
• Cooks food uniformly
• If frequency was higher
• waves would be absorbed too strongly by food and
  wouldnt penetrate deep into large items
• If frequency was lower
• waves would pass through food too easily and
  wouldnt cook efficiently
• Water molecules orient back and forth
• Liquid water heats due to molecular friction
• Ice doesnt heat due to orientational stiffness
• Steam doesnt heat due to lack of friction
• Foods liquid water content heats the food

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Effects of Microwaves

• Non-Conductors Polarization
• Mobile, polar molecules orient and heat
• Immobile, polar molecules do nothing much
• Non-polar molecules do nothing much
• Ceramic plates, glass cups, plastic containers
  are water-free and so remain cool
• Conductors Current flow
• Good, thick conductors reflect microwaves
• Poor conductors experience resistive heating
• Thin conductors experience resistive heating
• Can you put metals in a microwave oven?

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Metal in a Microwave oven

• The walls of the ovens cooking chamber are metal
• The walls reflect microwaves
• E fields in microwaves cause mobile charges in
  metal surfaces to accelerate and absorb the
  original microwaves
• As these charges accelerate, they emit new
  microwaves
• Same frequency as original waves, but new
  direction
• As long as the wavelength of the wave is much
  larger than the holes in the metal grid covering
  the window, the wave will reflect perfectly from
  that grid

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More on metals

• If you wrap food in aluminum foil, why wont the
  food cook?
• The waves are reflected
• What if you place food in shallow metal dish?
• Microwaves enter top pass through the food,
  reflect, and pass through the food again
• What about a sharp metal object?
• As you know, this is bad. Charge is pushed onto
  the sharp point and some of it will jump into the
  air as a spark.

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Question

• Why do microwave ovens not always cook evenly?

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Interference

• Identical waves that overlap can interfere
• Interference is when the fields add or cancel
• Adding fields are constructive interference
• Canceling fields are destructive interference
• Reflects cause interference in a microwave
• Interference causes uneven cooking
• Good microwaves stir waves or move food

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How are microwaves created in the oven?

• The source of microwaves is called a Magnetron
• Oven creates an alternating current at 2.5GHz
• This current causes charge to move in a tank
  circuit (last week) and moves charges up and down
  an antenna
• Basically what happens inside the magnetron tube

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Inside the Microwave
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Magnetron

• The magnetron is a diode-type electron tube which
  is used to produce the required 2450 MHz of
  microwave energy.
• Magnetron tube has tank circuits in it
• Resonant cavities
• Streams of electrons amplify tank oscillations
• A loop of wire extracts energy from tanks
• A short ¼-wave antenna emits the microwaves

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Magnetron

• Microwaves typically have 8 resonant cavities
• Carefully adjusted size and shape to have a
  natural resonance at 2.5GHz
• Cavities arranged in a ring
• Each one shares tips with neighboring cavities
• Oscillate alternately
• Cycle
• Start with half metal tips charged and other
  half - charge
• Currents flow through ring and produce magnetic
  fields in resonant cavities
• B fields propel currents around the ring
• and - tips interchanged

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Magnetron

• Both magnetic and electric fields are employed in
  the magnetron
• They are produced in perpendicular directions so
  that they cross.
• The applied magnetic field is constant and
  applied along the axis.
• The power to the device is applied to the center
  cathode which is heated to supply energetic
  electrons which would, in the absence of the
  magnetic field, tend to move radially outward to
  the ring anode which surrounds it.

The magnetron also includes a large permanent
magnet
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Magnetron

• Electrons are released at the center hot cathode
  and have an accelerating field which moves them
  outward toward the anode.
• The axial magnetic field exerts a magnetic force
  on these charges which is perpendicular to their
  initially radial motion, and they tend to be
  swept around the circle.
• In this way, work is done on the charges and
  therefore energy from the power supply is given
  to them.

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Magnetron

• As these electrons sweep toward a point where
  there is excess negative charge, that charge
  tends to be pushed back around the cavity,
  imparting energy to the oscillation at the
  natural frequency of the cavity.
• This driven oscillation of the charges around the
  cavities leads to radiation of electromagnetic
  waves, the output of the magnetron.

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Magnetron

• If there was only an E field, electrons would
  emerge the cathode and accelerate towards the
  tips of the cavities as beams of electrons.
• If there were no other fields besides the B field
  inside the magnetron, electrons would experience
  only Lorentz forces perpendicular to their
  velocities and would circle around the magnetic
  flux lines in counter-clockwise loops
• This is called cyclotron motion
• But in a magnetron E field and B field are
  present simultaneously

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Transport of energy by electromagnetic waves

• Electromagnetic waves carry energy as they
  travel through empty space.
• There is an energy density associated with both
  the electric and magnetic fields.
• The rate of energy transport per unit area is
  described by the vector
• which is called the Poynting vector.
• This expression is a vector product, and since
  the magnetic field is perpendicular to the
  electric field, the magnitude can be written

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Transport of energy by electromagnetic waves

• The rate of energy transport S is perpendicular
  to both E and B and in the direction of
  propagation of the wave.
• A condition of the wave solution for a plane wave
  is
• so that the average intensity for a plane wave
  can be written
• This makes use of the fact that the average of
  the square of a sinusoidal function over a whole
  number of periods is just 1/2.

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The 3K Cosmic Background Radiation

• Of great astrophysical significance is the 3K
  background radiation in the universe, which is in
  the microwave region.
• A uniform background radiation in the microwave
  region of the spectrum is observed in all
  directions in the sky.
• It has recently been mapped with great precision
  by the WMAP probe (Wilkinson Microwave Anisotropy
  Probe).
• The discovery of the 3K microwave background
  radiation was one of the crucial steps leading to
  the calculation of the standard "Big Bang" model
  of cosmology.
• The blackbody radiation is seen as a remnant of
  the transparency point at which the expanding
  universe dropped below about 3000K so that
  radiation could escape.

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The Microwave Sky
http//map.gsfc.nasa.gov/index.html

• Detailed picture of the infant universe. Colors
  indicate "warmer" (red) and "cooler" (blue)
  spots. The white bars show the "polarization"
  direction of the oldest light. This new
  information helps to pinpoint when the first
  stars formed and provides new clues about events
  that transpired in the first trillionth of a
  second of the universe.
• The expansion of the universe over most of its
  history has been relatively gradual. The notion
  that a rapid period "inflation" preceded the Big
  Bang expansion was first put forth 25 years ago.
  The new WMAP observations favor specific
  inflation scenarios over other long held ideas.
• WMAP data reveals that its contents include 4
  atoms, the building blocks of stars and planets.
  Dark matter comprises 22 of the universe. This
  matter, different from atoms, does not emit or
  absorb light. It has only been detected
  indirectly by its gravity. 74 of the Universe,
  is composed of "dark energy", that acts as a sort
  of an anti-gravity. This energy, distinct from
  dark matter, is responsible for the present-day
  acceleration of the universal expansion.

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A problem

• The electrons in a magnetron orbit the magnetic
  field at 2.5GHz, and as they do so they emit
  2.5GHz EM waves.
• What is the magnetic field strength?
• What is the maximum kinetic energy, if the
  maximum diameter of the electron orbit before the
  electron hits the wall of the tube is 2.5cm?
• Assume cyclotron motion.

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Answer
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Summary

• Microwaves are radio waves of 2.5GHz
• Water molecules are electrically polarized
• A magnetron provides the source of microwaves to
  the oven
• Quiz 2 today
• HW5 due Monday March 2
• http//www.colorado.edu/physics/2000/microwaves/in
  dex.html
• http//www.amasci.com/weird/microexp.html