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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