20.1) Induced emf and magnetic flux

  emf - electromotive force
  
  flux - noun form of the word 'flow'
  
  Faraday's experiment - electric wire coiled around an iron ring.  Another
  coiled wire at the other end of the ring with a galvanometer attached to it.
  When the first circuit is turned on or off, it induced a change in the 
  magnetic field, thus inducing a current in the other wire.
  
  An emf is produced in the second circuit by the changing magnetic field.
  
  Magnetic flux - 
  
  Φ ≡ BA cosθ
  
  
20.2) Faraday's Law of Induction

  Experiment - a single coil of wire is attached to a galvanometer.  When a 
  magnet is in motion through the loop, a current is induced.  The direction of
  motion determines the sign (+ or -) of the current.
  
  equation for emf:
  
  Ε = -N ΔΦ/Δt
  
  Where N is the number of coils, Φ is the magnetic flux; and t is time.
  
  Applications - guitar strings, SIDS devices
  
  
  
20.3) Motional EMF

  E=vB
  
  Where E is the Electric force, v is the velocity, and B is the strength of 
  the magnetic field.
  
  ΔV = El = Blv
  
  The change in Voltage is equal to the Electric force times the length of the
  wire.
  
  Experiment : a free sliding bar is attached to two parallel and attached
  conductors.  The whole thing is within a magnetic field.  When the free
  sliding bar is moved, a current is produced.
  
  In this case:
  
  |Ε| =  ΔΦ/Δt = BlΔx/Δt = Blv
  
  Where Ε is the motional Emf, x is the distance that the bar is moved.
  
  If the resistance in that circuit is R, then the current is:
  
  I = Ε/R = Blv/R
  
 
  
20.4) Lenz's Law

  The induced current must be in a direction such that the flux it produces
  opposes the change in magnetic flux.
  
  Consider the several different situations on p.661 in light of this law.
  
20.5) Generators 

  An AC generator in its simplest form consists of a rotating conductor
  inside a magnetic field.  That conductor is connected to rings, which
  rotate around another conductor.  The rotation within the magnetic field 
  causes a change in flux, which induces a current in the wire.
  
  Ε = NBAω sin ωt
  
  Where ω is the angular speed.
 
  A DC generator is very similar, except that the rings are split.  This causes
  the current to move in only one direction.  However, it is pulsating, but
  always in the same direction.
   
  Motors and back EMF
  
  A motor is a generator run in reverse.
  
  A current is applied to the loop which causes it to rotate because the of the
  fact that it is inside a magnetic field.
  
21.7) The AC transformer

  To transform voltage or current, the current source is coiled around a 
  conductive ring, the other end of the ring has another coil around it.  A
  current is induced in this second wire.  

  ΔV2 = ΔV1 N2/N1

  Therefore:
  I1ΔV1 =I2ΔV2
  
  This assumes a perfect transformers.  Real transformers are between 90% and 99%
  efficient.
  
21.8) Maxwell's predictions

  Based on these known facts:
  
  1) Electric field lines originate at positive charges and end at negative 
  charges
  2) Magnetic field lines formed closed loops
  3) Varying magnetic field induces an emf and hence an electric field.
  4) Magnetic field are generated by moving charges
  
  He predicted that electric and magnetic fields play symmetric roles in 
  nature.
  
  He also proved that both electric and magnetic field travel at the speed of
  light in a vacuum, and that light itself is an electromagnetic wave.
  
21.9) Hertz's discovery  
   
  When a capacitor is fully charged,
  
  E = Qm2/2C
  
  Where Qm is the charge in the capacitor, and C is the capacitance.
  
  When the current discharge, the energy is transferred to the magnetic field:
  
  E = LI2/2
  
  Where L is the inductive resistance of the inductor, and I is the current.
  
  The frequency of oscillation of such a circuit can be calculated.
  
  fo = 1/2Π sqrt(LC)

21.10) Production of electromagnetic waves in an Antenna

  An oscillating current is applied to an antenna.  The current produces an
  oscillating magnetic field.  
  
  In these waves, the electric field is perpendicular to the magnetic field.
  (We talked about this when we talked about polarization)

21.11) Properties of Electromagnetic waves

  c = 1/sqrt(μ0ε0)
  c = 2.99792 x 10 8 m/s
  
  E/B = c
  
  the ratio of the electric field to the magnetic field equals the speed of 
  light.
  
  p = U/c    (complete absorption)
  
  Where p is the momentum transmitted by electromagnetic waves hitting an
  absorber, and U is the total energy, and c is the constant speed of light.
  
  p=2U/c    (complete reflection)
  
  Reflector and absorption experiment
  
  Summary
  
  1) Electromagnetic waves travel at the speed of light
  2) EM waves are transverse
  3) ratio of E to B is c
  4) EM waves carry both energy and momentum, which can be delivered to a surface
  
21.12) Spectrum of Electromagnetic Waves

  c = fλ

  See chart p. 710.
  from longest to shortest wavelength
  radio
  microwaves
  Infrared (heat waves) longest wavelength
  visible light violet has shortest wavelength, red has longest
  UV
  X-rays
  gamma rays
  
21.12) Doppler effect for electromagnetic waves

  the speed of light is a constant from All reference points, even if the
  reference point is moving
  
  The frequency and wavelength can change.
  
  f' = f(1 ±u/c)
  
  u is the relative speed of the observer
  c is the speed of light in a vacuum, 3.0 x 108 m/s.
  
 
   
  
HW 14:
p. 675 CQ # 1,2   
p. 676 # 1
p. 677 # 10
p. 677 # 17
p. 717 # 35
p. 718 # 44