Chapter 23 – Electromagnetic Waves

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					Electromagnetic Waves   1
   Administrative
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   Begin Chapter 23 – Electromagnetic Waves
   No 10:30 Office Hours Today. (Sorry)
   Next Week … More of the same.
   Watch for still another MP Assignment
    ◦ Will they ever stop??? (No)



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      What do we learn from this?
                             6


 Some of you studied.
 Some of you didn’t.
 If you didn’t, do.
   Or         take my Studio Class in the Spring!




Electromagnetic Waves
   Electric Fields and Potential
   Magnetic Fields
   The interactions between E & M
   E&M Oscillations (AC Circuits/Resonance)

   James Clerk Maxwell related all of this
    together is a form called Maxwell’s Equations.




                             Electromagnetic Waves   7
    James Clerk Maxwell
   1831 – 1879
   Electricity and magnetism
    were originally thought to
    be unrelated
   In 1865, James Clerk
    Maxwell provided a
    mathematical theory that
    showed a close relationship
    between all electric and
    magnetic phenomena
   Electromagnetic theory of
    light


                                  Electromagnetic Waves   8
Maxwell Equations


closed surface     enclosed charge          closed surface               no mag. charge




   closed loop        linked flux           closed loop            linked current + flux


• Conservation of energy                 • Conservation of charge




                            Lorentz force law




                                                Electromagnetic Waves                      9
   When an E or B field is changing in time, a
    wave is created that travels away at a speed c
    given by:
                    1
              c             3  108 m / s
                    0 0

   This is the experimental value for the speed
    of light. This suggested that Light is an
    Electromagnetic Disturbance,
   In depth experimental substantiation
    followed.

                                         Electromagnetic Waves   10
   Can travel through empty space or through
    some solid materials.
   The electric field and the magnetic field are
    found to be orthogonal to each other and
    both are orthogonal to the direction of travel
    of the wave.
   EM waves of this sort are sinusoidal in nature.
    ◦ Picture a sine wave traveling through space.




                                  Electromagnetic Waves   11
Hertz’s Confirmation of
Maxwell’s Predictions
   1857 – 1894
   First to generate and
    detect electromagnetic
    waves in a laboratory
    setting
   Showed radio waves
    could be reflected,
    refracted and diffracted
    (later)
   The unit Hz is named for
    him


                               Electromagnetic Waves   12
   An induction coil is
    connected to two large
    spheres forming a
    capacitor
   Oscillations are initiated
    by short voltage pulses
   The oscillating current
    (accelerating charges)
    generates EM waves
   Several meters away
    from the transmitter is
    the receiver
    ◦ This consisted of a single
      loop of wire connected to
      two spheres

   When the oscillation frequency of the
    transmitter and receiver matched, energy
    transfer occurred between them
   Hertz hypothesized the energy transfer was in
    the form of waves
    ◦ These are now known to be electromagnetic waves
   Hertz confirmed Maxwell’s theory by showing
    the waves existed and had all the properties of
    light waves (e.g., reflection, refraction,
    diffraction)
    ◦ They had different frequencies and wavelengths which
      obeyed the relationship v = f λ for waves
    ◦ v was very close to 3 x 108 m/s, the known speed of
      light
   Two rods are connected to an oscillating source, charges
    oscillate between the rods (a)
   As oscillations continue, the rods become less charged, the field
    near the charges decreases and the field produced at t = 0
    moves away from the rod (b)
   The charges and field reverse (c) – the oscillations continue (d)
   Because the oscillating charges in
    the rod produce a current, there is
    also a magnetic field generated
   As the current changes, the
    magnetic field spreads out from
    the antenna
   The magnetic field is
    perpendicular to the electric field
 A changing magnetic field produces an
  electric field
 A changing electric field produces a magnetic
  field
 These fields are in phase
    At any point, both fields reach their maximum value
     at the same time
Electromagnetic Waves   19
Electromagnetic Waves   20
Was It Magic?
        Electromagnetic Waves   21
Electromagnetic Waves   22
• The waves are transverse:
electric to magnetic and both
to the direction of
propagation.
•The ratio of electric to
magnetic magnitude is E=cB.
•The wave(s) travel in vacuum
at c.
•Unlike other mechanical
waves, there is no need for a
medium to propagate.
   The old RH-Rule
    ◦ turn E into B and
      you get the
      direction of
      propagation c.
    ◦ Rotate c into E and
      get B.
    ◦ Rotate B into c and
      get E.




                            Electromagnetic Waves   26
l




    Electromagnetic Waves   27
Electromagnetic Waves   28
Electromagnetic Waves   29
   Seeing in the UV, for example, steers insects to
    pollen that humans could not see.




                                Electromagnetic Waves   30
Electromagnetic Waves   31
Electromagnetic Waves   32
Two types of waves




                     Electromagnetic Waves   33
      LikeSound Waves,the equation
         for a moving EM wave is :
                 t x
E  E m axSin(2    )  Em axSin(t  kx)
                 T l 
                 t x
B  Bm axSin(2    )  Bm axSin(t  kx)
                 T l 
                      2
                   k
                          l
                 Em ax  cBm ax
                        c
                     l
                        f

Suggestion – Look again at the
chapter on sound to solidify
this stuff.
                                      Electromagnetic Waves   34
  V  c t

How much Energy
is in this volume?




                     Electromagnetic Waves   35
Light carries

Energy

and

Momentum




                Electromagnetic Waves   36
&




    Electromagnetic Waves   37
   Energy 1       1
u        0E 
              2
                     B 2
   Volume 2      20

      From before
          E  cB

  E    E
B                   E  0 0
  c  1
             0 0
      B 2   0 0 E 2

                                  Electromagnetic Waves   38
           So.
           B 2   0 0 E 2
                    ng
           Substituti into the previous,
              1         1
           u  0E 2
                             0 0 E 2
              2        20
           or
              1     1
           u  0E  0E2  0E2
                  2
              2     2

Energy stored in the B and B fields are the same!


                              Electromagnetic Waves   39
• Electric and magnetic fields contain energy,
potential energy stored in the field: uE and uB
uE: ½ 0 E2 electric field energy density
uB: (1/0) B2 magnetic field energy density

•The energy is put into the oscillating fields by
the sources that generate them.

•This energy can then propagate to locations
far away, at the velocity of light.
Energy per unit volume is                          B

                                       dx
u = uE + uB    1 (  0 E 2  1 B2 )
                2             0            area
                                                       E
                                            A
Thus the energy, dU, in a box of
area A and length dx is
           1
     dU  ( 0 E 2  1 B2 ) Adx      c         propagation
           2         0                        direction

Let the length dx equal cdt. Then all of this energy leav
the box in time dt. Thus energy flows at the rate
    dU 1          1 2
        ( 0 E 
               2
                     B ) Ac
     dt 2         0
                                                 B
Rate of energy flow:
                                     dx
   dU c           1 2
        ( 0 E 
               2
                     B )A
    dt  2         0                      area
                                          A
                                                      E

We define the intensity S, as the
rate of energy flow per unit area:

      S   c (  E 2  1 B2 )        c      propagation
           2    0
                       0                   direction

Rearranging by substituting E=cB and B=E/c,
we get,
 S  c (  cEB  1 EB )  1 (   c 2  1 )EB  EB
     2 0            0c       20 0 0               0
                                                B
In general, we find:
                                dx
    S = (1/0) EB                     area
                                                     E
                                      A

S is a vector that points in the
direction of propagation of the 
wave and represents the rate of
                                S
                                             propagation
energy flow per unit area.                   direction
We call this the “Poynting vector”.

Units of S are Jm-2 s-1, or
Watts/m2.
          The Inverse-Square Dependence of S
  A point source of light, or any radiation, spreads
  out in all directions:                   Power, P, flowing
                                              through sphere
             Source                           is same for any
                                              radius.


              P
         S 
             4r 2

Source
                        r
                                               Area  r 2
                                                  1
                                               S 2
                                                 r
Intensity of light at a distance r is           S= P / 4r2
      P       1 2
I               Erms
     4r 2   0 c

           P0 c   ( 250W )( 4 107 H / m )( 3108 m / s )
                                               .
 Erms          
           4r 2                 4 ( 18m )2
                                       .

 Erms  48V / m

         Erms    48V / m
B                8m / s
                            0.16 T
          c      .
                310
• When present in
large flux, photons
can exert
measurable force on
objects.
• Massive photon
flux from excimer
lasers can slow
molecules to a
complete stop in a
phenomenon called
“laser cooling”.
Momentum and energy of a wave
are related by, p = U / c.

Now,    Force = d p /dt = (dU/dt)/c

pressure (radiation) = Force / unit area

P = (dU/dt) / (A c) = S / c

 Radiation Pressure  Prad      S
                                  c
               Polarization
The direction of polarization of a wave is
the direction of the electric field. Most light
is randomly polarized, which means it
contains a mixture of waves of different
polarizations.
      Ey

  B                           Polarization
  z                           direction


                               x
                 Polarization
A polarizer lets through light of only
one polarization:
        E0              E                Transmitted light
    q                                    has its E in the
                                         direction of the
                                         polarizer’s
                                         transmission axis.



             E = E0 cosq

             hence,   S = S0 cos2q

                       - Malus’s Law
                        At least of this
                        chapter.

Electromagnetic Waves                      50

				
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