Download Physics 202, Lecture 23 Electromagnetic Waves Energy Carried By

Electromagnetic Waves
Physics 202, Lecture 23
E
  EM wave equations:
Today’s Topics
z
 Electromagnetic Waves (EM Waves)
  Properties of EM Wave (review)
  Energy Carried by EM Wave, Poynting Vector
  Momentum Carried by EM Wave
 Review for Exam 3
 Next lecture: Light and Optics, Ch 35. Professor Pan
will give the lectures for the rest of the semester.
Energy Carried By EM Waves
  right hand rule again!
  Power per unit area [J/s•m2 = W/m2]
  S= 1/µ0 EB =uc
B
 Plane wave solutions:
E= Emaxsin(kx-ωt+φ)
B= Bmaxsin(kx-ωt+φ)
 Properties:
  No medium is necessary.
same φ,
  E and B are normal to each other
set to be 0
  E and B are in phase
  Direction of wave is normal to both E and B
(EM waves are transverse waves)
  Speed of EM wave:
  E/B = Emax/Bmax=c
  Transverse wave: two polarizations possible
y
S
z
x
  Recall: energy densities uE= ½ ε0E2, uB= ½ B2/µ0
  For a EM wave, at any time/location,
uE = ½ ε0E2 = ½ B2/µ0 =uB (using E/B=c)
 In an electromagnetic wave, the energies carried by
electric field and magnetic field are always the same.
  Total instantaneous energy per unit volume:
u = uE + uB = � 0 E 2 =
  Intensity: take average over time.
2
Emax Bmax
E2
cBmax
=
= max =
2µ0
2µ0 c
2µ0
B2
µ0
  Total average energy per unit volume:
2
uavg = �0 (E )avg
I = savg
x
Energy Carried By EM Waves
  Poynting vector: describes the rate of transfer of energy
(power) by EM wave. Instantaneous rate at which energy
is passing through unit area.
S= 1/µ0 ExB
c
B
E
y
E
B
1
B2
2
= �0 Emax
= max z
2
2µ0
y
S
x
  Power transmitted per unit of area (flux)
is equal to uc in the direction of wave
I = savg = uavg c
1
S
Momentum Carried By EM Waves
  EM waves: momentum = energy/c
A
ΔX=cΔt
Change of momentum in
100% absorption
Example: Solar Radiation (sun light)
 The average intensity of the EM radiation from the
Sun on Earth is S ~ 103 W/m2
  What is the average radiation pressure for 100%
absorption?
Change of momentum in
100% reflection
 Radiation Pressure (P):
100% absorption
100% reflection
Δp = p  P= S/c
Δp = 2p  P= 2S/c
  What is the force exerted by EM radiation by the
Sun on a surface of 1 m2 (with 100% absorption)?
Mariner 10: “Sail on sunlight”
Spherical Waves and Plane Waves
  Spherical EM waves: Radiation from a point source.
 By laws of energy conservation, intensity (flux) of
spherical EM waves goes as ~1/r2.
About Exam-3
  When and where
  Monday April 18 5:30-7:00 pm
  Location: Same as last time.
•  Ingraham B10: Sections 301, 302, 303, 304, 305, 307, 309, 322, 323
•  Van Vleck B102: Sections 308, 310, 324, 325, 326, 327, 329, 330
spherical wave
  Plane waves: Beams are in parallel.
 Intensity (flux) of plane EM waves remains
as a constant.
plane wave
  Format
  Closed book, 20-25 multiple-choices questions , same style as
midterm 1.
  1+1 8x11 formula sheet allowed, must be self prepared, no photo
copying/download-printing of solutions, lecture slides, etc.
  Bring a calculator (but no computer). Only basic calculation
functionality can be used. Bring a 2B pencil for Scantron.
  Write down and bubble your ID and section #
  Special requests:
  All requests for specially arranged tests must be made by noon
today and are held in our 202 labs. (for approved testers only)
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Exam-3: Chapters Covered
  Ch 31: Faraday’s Law (all sections)
  Ch 32: Inductance (all sections)
  Ch 33: Alternating-Current Circuits (33.1 – 33.7, RC time
constant)
  Ch 34: Electromagnetic Waves (all sections)
  Basics of waves from ch 16 may be useful
  Material from HW11 (due 4/20) will be on the exam.
Suggested preparations:
  Homework problems
  Homework problems again
  “Quick quiz” for conceptual understanding
  Additional problems at the end of chapters
  Pay special attention to signs and directions!
Reviews:
  This lecture
  There will be additional office hours on Friday, Sat/Sun in the lab rooms.
Ch34 representative questions
(not meant to be complete)
  HW 11.
  Rate of change of electric flux given capacitor or some
other electric field configuration, the resulting
displacement current.
  How are magnitude of B and E field related in EM waves?
  Given λ, what is f? or vice versa
  Given E (or B) = A sin(kx-wt), what is the amplitude of B
(or E), λ, f, etc.
  What would be the length of a λ/4 antenna if I want to
transmit ##MHz radio waves?
  What is the maximum radiation pressure exerted by
(some light source like sun, laser pointer, light bulb of
given intensity) on reflective surface or absorbing
surface?
Ch. 34: EM waves
 Maxwell’s equations + Lorentz force law
 Plane EM waves
  Wave equations
  Speed of light
  E/B = c
  c = λf
 Energy carried by EM waves
  Poynting vector, intensity
 Momentum and radiation pressure
 Production of EM waves by an antenna (λ/4)
 EM wave spectrum
  Visible, radio, IR, x-ray, etc.
Ch 31: Faradays’ Law
 Faraday’s law of induction
 Lenz’s law
  Induced current and induced emf in a conductors
are in such a direction as to set up a magnetic
field that opposes the change that produces them.
 Motional emf
 Generators and motors
 Eddy currents
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Ch31 representative questions
 HW 7 & 8
 Given changing magnetic field spanning some area,
what is the emf induced? Current in N coils with
resistance R? Direction?
 Given constant magnetic field but changing area,
what is the induced emf? Current? Direction?
 Given constant magnetic field and coil but coil is
rotating (e.g. generator), what is emf, current,
direction?
 Sliding bar circuit in magnetic field: What is the force
required to keep the bar moving at a constant
velocity? (motional emf)
Ch32 representative questions
  HW 9
  Given inductance and current that is changing, what is
the induced emf at certain time?
  Given R and L plus a battery, what is the current at
certain time after the switch is closed? When does the
current reach xx% of the final value?
  In a RL circuit, what is the potential across R? L?
compare the two.
  What is the inductance of a coil(s)? Air-core solenoid?
  How much energy is stored in the magnetic field of a
solenoid given its dimensions, number of turns and
current?
  What is the mutual inductance of two solenoids given
number of turns, flux, and current? Induced emf?
  Frequency of LC circuit, RLC circuit
  Critical resistance of RLC circuit, behavior when R >
Rcritical, R < Rcritical, R = Rcritical,
Ch. 32 Inductance
 Self-Induction and Inductance: ε0 = -L*dI/dt
 RL Circuits
  I = Imax(1-e-t/τ), I = = Imax(e-t/τ), τ = L/R
 Energy in a magnetic field
  U = ½ LI2, uB = B2/(2µ0)
 Mutual inductance
  M12 = N2Φ12/I1 = M21 = N1Φ21/I2=M
  ε2 = -M12dI1/dt , ε1 = -M21dI2/dt ,
 Oscillations in an LC Circuit: ω = 1/sqrt(LC)
 RLC Circuit
  General behavior, resonant frequency
Ch 33: AC Circuits
 Resistors, inductors, & capacitors in AC circuit
  Capacitive reactance (XC), inductive reactance (XL)
  Impedance Z = sqrt(R2+(XL-XC)2)
  Phase angle between current and voltage:
•  φ=tan-1((XL-XC)/R)
  Irms, Vrms
 RLC Series circuit
 Power in an AC Circuit
 Resonances in a series RLC circuit
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Ch33 representative questions
 Rms current and voltage
 Given R, L, C, what is the power delivered in an AC
circuit?
 Resonant frequency?
 Given R, L, & C, what are the inductive and
capacitive reactance? Impedance? Phase?
 What is the maximum current in a L or C circuit for a
given Vrms and f?
 In RLC circuit, what is the voltage across R, L, C for
a given Vrms and f?
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