Ch 32 Maxwells Equations

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Ch 32 Maxwells Equations
1831-1879 (Edinburgh, Scotland) The first
Unification of Physical Laws. The pursuit has
never stopped.

• 1)Gauss Law for s Electrostatics
• 2)Gauss Law for Magnetostatic
• 3)Faraday's Law
• 4)Maxwell-Ampere Law
• They predict that light is an EM Wave
  propagating at speed 3x108 m/s

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Can you ever just get a north pole or a south
pole ???
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Gausss Law for Magnetism

• Reminder of the definition of magnetic flux

As of today 4/21/05 there is no evidence of
magnetic monopoles See Phys.Rev.Lett.855292,2000

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Gausss Law for Magnetism

• Only magnetic dipoles exist

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The Search for magnetic monopoles Goes ON!
Null result sets the lower bound on a monopole
mass to be about m295-495 GeV
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Carl Friedrich Gauss 1777-1855
The total flux passing through a closed surface
is proportional to the charge enclosed within
that surface.
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KEY TO USING Gausss Law

• The shape of the surrounding surface is one that
  MIMICS the symmetry of the charge distribution ..

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Faraday Changing Flux due to moving permanent
magnet
1791-1867 British Physicist
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Induced EMF produced by a changing Magnetic
Flux!
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Induced electric fields
We will assume here that B is increasing into
the page
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Electric Field circulates about a changing
magnetic field (into the page here)
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Maxwell thought is there a symmetry here? Can
there be a circulating magnetic field around a
changing electric field?
Maxwells Law of Induction
WAIT!!! Didnt we already see that B circulates
around a current carrying WIRE ?!!?
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Recall Amperes Law Andre Marie Ampere
(1775-1836)
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Long Straight Wire with a constant current
For rgtR, radius of wire the magnetic field must
have cylindrical symmetry
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Ampere-Maxwell Law and Maxwells Displacement
current
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Displacement Current
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Maxwells Equations
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Information AGE, Medicine, Engineering .

• Based on the physics of EM waves
• T.V. telecommuncations, radio transmission, radar
  
• Challenge of todays engineers to try to envision
  what global interconnections will be in 20 years
  (Halliday and Resnick 04)
• Starting point understanding Electro-mag waves
  which is summarized by Maxwells rainbow!

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EM Waves and Maxwell

• Crowning achievement was to show that light is a
  traveling EM wave
• The basis for the study of optics! Phys. 213 and
  Dr. Romberger Phys. Science 440
• In mid 1800s only infrared, visible and
  ultraviolet forms of light were only EM waves
  know
• Heinrich Hertz later showed that what we call
  radio waves also ..

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Maxwells Rainbow
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Human Eye Sensitivity
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Traveling Waves
Consider a transformer A generating LC circuit
which establishes a frequencey and a secondary
coil with a dipole antenna. You have a changing E
and B field coupled together!!! However, changes
dont appear instantaneously, they happen a the
speed of light with the disturbance traveling
outward at that speed. Will see
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Looking toward the wave front the amplitudes are
related by the cross product Wave is
transverse/perpendicular to the direction of
travel Field vary sinusoidally
At speed of light!!
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Traveling EM waveNo need for a medium on wave
generates the other. Prediction of Maxwells
equation and proved by Einstein with a little bit
of symmetry 1905 Phys. 214 next Fall!!!
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Faradays Law of InductionMaxwells Law of
Induction
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Faradays Law of induction
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Maxwells Law of induction
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The Wave Equation

• Source free region ie no wires and no charges

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Spherical WaveEnergy