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About Exam 3 When and where (same as before)
Monday Nov. 22rd 5:30-7:00 pm Bascom 272: Sections 301, 302, 303, 304, 305, 311,322, 327, 329 Ingraham B10: Sections 306, 307, 312, 321, 323, 324, 325, 328, 330
Format (same as before) Multiple choices Close book One 8x11 formula sheet allowed, must be self prepared. Bring a calculator (but no computer). Only basic calculation
functionality can be used. Special needs:
No early test before Monday Nov 22rd possible. One alternative session (Monday afternoon) in our lab room Please email me for request/approval before next Monday!
Physics 202, Lecture 21
Today’s Topics
Electromagnetic Waves (EM Waves) Maxwell’s equation Speed of EM Waves The Hertz Experiment EM Wave Spectrum, Wavelength and Frequency
Antenna How to make a “HDTV” Antenna?
Sources of E and B Fields
Sources for the electric field: Electric charges (Coulomb's Law, static)
subjects of past several weeks Change of B field (Faraday's Law, varying in time)
Sources for the magnetic field: Electric current (Biot-Savart Law/Ampere’s Law, static) Change of E field (Ampere-Maxwell Law, varying)
All these features are summarized in Maxwell Equations.
Maxwell Equations Gauss’s Law/ Coulomb’s Law
Faraday’s Law
Gauss’s Law of Magnetism, no magnetic charge
Ampere-Maxwell Law
Also, Lotentz force Law
These are the foundations of the electromagnetism
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Ampere’s Law Revisited A magnetic field is produced by an electric current is
given by the Ampere’s Law
A changing electric field will also produce a magnetic field Finally;
“Displacement current”.
µ0: permeability of free space (also a constant)
ε0: permittivity of free space (a constant)
Demo: Hertz Experiment
In 1887, Heinrich Hertz first demonstrated that EM fields can transmit over space.
EM Fields in Space Maxwell equations when there is no charge and current:
differential forms: (single polarization)
x
y
z
E
B
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Fig. 34-6, p. 989
Linear Wave Eq. and Solutions (Ch. 16)
Wave function for a propagating wave: y(x,t) = f(x-vt)
Linear Wave equation and harmonic waves
Wave speed A:Amplitude
f: frequency φ:Phase
v=λf k=2π/λ ω=2πf
λ:wavelength
Solution
Wave speed
Electromagnetic Waves EM wave equations:
Plane wave solutions: E= Emaxcos(kx-ωt+φ) B= Bmaxcos(kx-ωt+φ)
x
y
z
E
B c
Two polarizations possible (here showing one)
Ec B=
Electromagnetic Waves Speed of EM wave:
EM wave can transmit in vacuum !
Wavelength and Frequency Relationship:
Great significance: 1. EM waves exist in vacuum; 2. Speed of wave (light) finite; 3. Superposition: interference, diffraction; 4. Polarizations.
In vacuum
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Spectrum of EM Waves λf=c f (Hz) λ
VHF: 30-300 MHz UHF: 300 MHz -3.0 GHz Cell phone: 800/900/1800/1900 MHz Wifi: 2.4/5 GHz Microwave Oven: 2.4 GHz Cordless phone: 0.9/2.4/5.8 GHz
MHz
GHz
Wavelength For TV Signals Wavelength and frequency relationship for EM wave
Example: Determine the wavelength (in air) of an EM wave of frequency 687 MHZ (HDTV channel 3, CBS = UHF ch. 50)
VHF: λ = 1-10 m , UHF: λ = 0.1-1 m Over-The-Air (OTA) DTV channels: 90% of them in UHF band λ ~ 0.4 - 0.6 m
In vacuum
Half-Wave Antenna
half-wave antenna
λ/4
λ/4
Standing Wave Condition (ch. 18) λ/4
λ/4
A special configuration ¼ -wave antenna
λ/4
ground
Co-axial cable
Various RF Antennas
loop
mocristrip