Electromagnetic waves

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Electromagnetic waves

• Bringing It All Together

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This Week

• Today-
• No Clickers sell them back to the bookstore
  unless you are planning to take my section of the
  course next semester. Bad idea!
• We tie the stuff together and do the candle trick
  right in front of you. (Remember the video??)
• The rest of the week FINAL EXAMS

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My schedule

• Tuesday Not on Campus
• Wednesday Friday
• Giving exams
• Grading Papers
• In foul mood! Stop by if you need to.
• Grades will be completed as fast as I can.
• Grader has finals this week to, so it may be a
  slow process.

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The Last LectureCovering 5 Additional Chapters

• We have been looking at the properties of
  Electric Fields.
• We have been looking at the properties of
  Magnetic Fields
• We looked at a few situations where there was
  some kind of connection between the two.
• We saw that ALL of what we discussed could be
  explained by one set of equations.
• MAXWELLs Equations

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James Clerk Maxwell

• 1831 1879
• Scottish physicist
• Provided a mathematical theory that showed a
  close relationship between all electric and
  magnetic phenomena
• His equations predict the existence of
  electromagnetic waves that propagate through space

SMART DUDE
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Almost Maxwell
Bindell
Gauss
Faraday
Ampere
EB Together
Problem
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Remember the Lowly Capacitor?
AC CurrentI
But there MUST be a magnetic field present
around the gap - even if it is small!
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• Ampères Law is used to analyze magnetic fields
  created by currents
• But this form is valid only if any electric
  fields present are constant in time
• Maxwell modified the equation to include
  time-varying electric fields
• Maxwells modification was to add a term

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Maxwell Fixed the Problem!

• The additional term included a factor called the
  displacement current, Id
• This term was then added to Ampères Law
• Now sometimes called Ampère-Maxwell Law
• This showed that magnetic fields are produced
  both by conduction currents and by time-varying
  electric fields

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MAXWELLS EQUATIONS
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Vacuum

• There aint nuttin there.
• No Charges
• No Currents
• Can there be electric or magnetic fields
  present??
• Maxwells equations say YES
• And they add some serious requirements to what is
  there.

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Sorry its crooked!
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Propagation Direction
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Back to Maxwell

• E M fields can propagate from a region where
  there are charges/currents to regions far away
  where they do not contain these sources.
• The fields propagate as WAVES
• Shape moves at the speed of the wave.
• Because the E field is changing (moving charge
  example), there will be a B field there as well.

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EnterHeinrich Rudolf Hertz

• 1857 1894
• German physicist
• First to generate and detect electromagnetic
  waves in a laboratory setting
• The most important discoveries were in 1887
• He also showed other wave aspects of light

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Hertz Experiment
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So far we can assume
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Extended View Sine Shape
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The Magic From Ms 4

• Mathematically these equations describe waves
  traveling thought space.
• E and B are perpendicular to each other and to
  the direction of propagation.
• The velocity of the wave must be

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The Velocity is c

• This must describe light waves ..

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It can be shown that the wave carries energy and
momentum,
Receiver!
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How??
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FINAL DEMO!