Download Guass`s Law for magnetism

Electromagnetic Waves
Chapter 35
Electromagnetic (EM) Waves
• Can travel through space
• Radio, Microwaves, IR, Light, UV, X-rays,
Gamma Rays
• All on the electromagnetic spectrum
James Clerk Maxwell
Maxwell’s Equations
1. Guass’s Law – The greater the charge,
the greater the electric field
2. Guass’s Law for magnetism Magnetic flux is zero through a closed
surface
3. Faraday’s Law – An electric field is
produced by a changing magnetic field
4. Ampere-Maxwell Law - A magnetic
field is produced by a changing electric
field (moving charge)
Guass’s Law
Guass’s Law for
magnetism
Faraday’s Law
Ampere-Maxwell Law
An electric field is produced by:
• Charged particle (moving or stationary)
• Changing magnetic field
A magnetic field is produced by:
• A curent (moving charge)
• Changing electric field
Lorentz Force
Results
• An electric field exerts a force on any charged
particle
• A magnetic field exerts a force on a moving
charged particle
Producing Electromagnetic Waves
DC case
• Current flows to either antenna
(like a capacitor)
• Electric field produced
• Magnetic field produced (right
hand rule)
AC case
• Changing direction of current
• Field line close up to form a loop
• Magnitude of E and B decrease with 1/r
• Energy is proportional to E2 or B2
EM Wave
• Sinusoidal
• E and B are perpendicular to one another
• E and B are in phase
• Accelerating electric charges produce
electromagnetic waves
Speed of EM Waves
v=
1
√eomo
eo = 8.85 X 10-12 C2/Nm2 (permittivity)
mo = 4p X 10-7 Ns2/C2
(permeability)
Calculate the speed of light using these constants
Wave Properties
• First man-made EM waves detected by Hertz (8
years of Maxwell’s death)
l = wavelength (meters)
f = frequency (cycles/s or Hertz)
fl=c
(in a vacuum)
Electromagnetic Spectrum
• Visible light
• 4 X 10-7 m to 7X 10-7 m (400 to 700 nm)
• Electrons
– Radio – running electrons up and down an antenna
– Electrons moving within atoms and molecules
– X-rays - Electrons are rapidly decellerated by striking
metal
• Gamma Rays – Nuclear decay
Waves: Ex 1
Calculate the wavelength of a 60 Hz EM wave
fl=c
l = c/f
l = (3.0 X 108 m/s)/60 s-1 = 5 X 106 m
What range of the spectrum is this?
Waves: Ex 2
Calculate the wavelength of a 93.3 MHz FM radio
station
fl=c
l = c/f
l = (3.0 X 108 m/s)/(93.3 X 106 s-1) = 3.22 m
Waves: Ex 3
Calculate the frequency of 500 nm blue light.
fl=c
f = c/ l
f = (3.0 X 108 m/s)/500 X 10-9 m = 6 X 1014 Hz
Waves: Ex 4
When you speak to a telephone to someone 4000
km away, how long does it take the sound to
travel?
v = d/t
t = d/v
T = (4000 X 103 m)/(3 X 108 m/s) = 1.3 X10-2 s
Speed is less because of wires
Measuring the Speed of Light
• Galileo – Tried to measure from mountaintop to
mountaintop.
• Roemer – Measured time needed for light to
travel from Io (Jupiter’s moon)
• Michealson’s Experiment
• Measured time needed for light to travel and be
observed
• Only certain rotational speeds allowed observer
to see the light
• Tried it on mountains in southern California (35
km)
c = 2.99792458 X 108 m/s
c = 3.0 X 108 m/s
• Slightly slower in air
• Same for all EM waves
Energy and EM Waves
• All EM waves carry energy
• Exactly half by electric field and half by magnetic
field
E = cB
(relates E and B)
S = ½ eocE2o = ½ cB2o
mo
(ave rate of energy transported per unit area, per
unit time)
Radio Transmitter
• Carrier Frequency – Frequency that one “tunes
in”
• AM - 530 to 1600 kHz
• FM – 88 to 108 MHz
• Broadcast TV - 54 to 88 mHz, 174 to 216 MHz
AM Radio
• Amplitude Modulated
• Program signal mixes with carrier signal
• Frequency of wave does not change, only
amlitude
FM Radio
• Frequency Modulated
• Frequency of total signal varies (slightly)
• 101.3 and 101.5 but never 101.4
Receiving a Signal
• Straight Antenna – Electric field of EM wave
produces a current in the electrons in the antenna
• Loop Antenna – Magnetic field of EM wave
induces a current
• Tune in a station – uses the resonant frequency of
an LC circuit (variable capacitors/inductors)
Radio: Ex 1
An FM station is 103.1 mHz. Calculate the
wavelength:
fl=c
l = c/f
l = (3.0 X 108 m/s)/(103.1 X 106 s-1) = 2.91 m
What is the value of the capacitance for this tuning
circuit if L = 0.40 mH?
fo = 1
2p √LC
C = 1/(4p2fo2L)
C = 1/ (4)(3.14)2(1.0x108