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Physics 102: Lecture 14, Slide 1
Electromagnetic Waves
Physics 102: Lecture 14
Physics 102: Lecture 14, Slide 2
Review: Phasors & Resonance
• At resonance– Z is minimum (=R)– Imax is maximum (=Vgen,max/R)– Vgen is in phase with I– XL = XC VL(t) = -VC(t)
• At lower frequencies– XC > XL Vgen lags I
• At higher frequencies– XC < XL Vgen lead I
Imax(XL-XC)
ImaxXL
ImaxXC
ImaxR
V gen,max
Physics 102: Lecture 14, Slide 3
Preflight 14.1As the frequency of the circuit is either raised
above or lowered below the resonant frequency, the impedance of the circuit:
Always increasesResonance in AC Circuits
frequency
Only increases for lowering the frequency
Only increases for raising the frequency
f0
Z
LR
C
Physics 102: Lecture 14, Slide 4
Preflight 14.3At the resonant frequency, which of the
following is true?
I is in phase with Vgenerator
I leads Vgenerator
I lags Vgenerator
VL
VC
VR
Vgen
Physics 102: Lecture 14, Slide 5
What is it good for?
• Current through circuit depends on frequency (maximum at resonance frequency fo)
– Radio receiver– Stereo equalizer– NMR/MRI
LR
C
Physics 102: Lecture 14, Slide 6
Resonance in Radios
An AC circuit with R= 2 , L = 0.30 H and variable capacitance is connected to an antenna to receive radio signals at the resonance frequency. If you want to listen to music broadcasted at 96.1 MHz, what value of C should be used?
LR
C
Physics 102: Lecture 14, Slide 7
ACT: RadiosYour radio is tuned to FM 96.1 MHz and
want to change it to FM 105.9 MHz, which of the following will work.
1. Increase Capacitance
2. Decrease Capacitance
3. Neither, you need to change R
Physics 102: Lecture 14, Slide 8
James Clerk Maxwell
1. E-field generated by electric charge(Gauss’ Law – Lecture 2)
2. No magnetic charges(Lecture 8)
3. E-field generated by changing magnetic flux(Faraday’s Law – Lecture 10)
4. B-field generated by moving electric charge
& changing electric flux! (Ampere’s Law – Lecture 9)
4 laws unify electric & magnetic forces:
(1831-1879)
Electromagnetic waves!
Physics 102: Lecture 14, Slide 9
Radio antennaGenerator creates oscillating current up and down metal rods
+
-I
x
y
This is called an electric dipole antenna
This is an electric dipole!
Physics 102: Lecture 14, Slide 10
Oscillating E fieldElectric dipole antenna creates an oscillating electric field
In which direction does the E-field point at this time?
NOT QUITE! E-fields do NOT appear everywhere in space instantaneously, they travel at a finite speed c
... and now?
Physics 102: Lecture 14, Slide 11
Electromagnetic radiation• E-fields do NOT appear everywhere in space instantaneously, they travel at a finite speed c
x
y
t=0t=T (one full period) = 1/f
cT =
c = f
ccEM wave!
Physics 102: Lecture 14, Slide 12
ACT: EM WavesWhich direction should I orient my antenna to
receive a signal from a vertical transmission tower?
1) Vertical 2) Horizontal 3) 45 Degrees
Direction wave travels
demo
Physics 102: Lecture 14, Slide 13
Electromagnetic radiation• Current in antenna also creates oscillating B-field• B-fields do NOT appear in space everywhere instantaneously they travel at a finite speed c
x
y
EM wave!
c = f
E and B fields propagate together as EM waves
II
Physics 102: Lecture 14, Slide 14
𝜇0 = 4𝜋× 10−7𝑇𝑚/𝐴
Recall fundamental constants of electricity and magnetism:
“Permeability of free space” (magnetism)
𝜀0 = 8.85× 10−12𝐶2/𝑁𝑚2
“Permittivity of free space” (electricity)
𝜀0𝜇0 = 8.85× 10−12 𝐶2𝑁𝑚2 × 4𝜋× 10−7 𝑇𝑚𝐴
Speed of EM wave in vacuum
Now multiply them:
𝜀0𝜇0 = 8.85× 10−12 𝐶2𝑁𝑚2 × 4𝜋× 10−7 𝑁𝑚𝐶𝑚/𝑠 𝐶/𝑠
= 1.11× 10−17 𝑠2𝑚2 Note: 1T = 1 N/Cm/s (from F = qvBsin(θ))1A = 1 C/s (from I = ΔQ/Δt)1
ඥ𝜀0𝜇0 = 3.0× 108𝑚/𝑠 c =
Physics 102: Lecture 14, Slide 15
Electromagnetic Waves
xz
y
• Transverse (vs. sound waves – longitudinal)
• E perpendicular to B and always in phase E & B increase and decrease at same times
• Can travel in empty space (sound waves can’t!)
• Speed of light in vacuum: v = c = 3 x 108 m/s
(186,000 miles/second!)
• Frequency: f = v/= c/Period: T = 1/f
Physics 102: Lecture 14, Slide 16
Preflight 14.6 – 14.12
Which of the following are transverse waves?
• sound
• light
• radio
• X-ray
• microwave
• water waves
• “The Wave” (i.e. at football games)
Physics 102: Lecture 14, Slide 17
Electromagnetic Spectrum• Light, Radio, TV, Microwaves, X-Rays are
all electromagnetic waves!
c = f
R O Y G B I V
Physics 102: Lecture 14, Slide 18
EM Waves Practice
E
x
Shown below is the E field of an EM wave broadcast at 96.1 MHz and traveling to the right.
(1) What is the direction of the magnetic field?
(2) Label the two tic marks on the x axis (in meters).
Perpendicular to E, v: Into/out of the page
3.1 6.2
Physics 102: Lecture 14, Slide 19
This picture only represents EM wave along one line (x-axis)
xz
y
Representing EM wave: Wavefronts
Imagine a slice in y-z planey
z E-field & B-field same everywhere along plane
Wavefronts – surfaces at crests of EM wave
Physics 102: Lecture 14, Slide 20
Doppler EffectNow the car is moving to the left.Observed wavelengtho different!
u
A police car emits light of wavelength e
e oe oe
Moving toward observer: fo = fe(1 + u/c)
Only relative velocity matters:u = v1 + v2 moving in opposite directions u = v1 – v2 moving in same direction
= f/cMoving away from observer: fo = fe(1 – u/c)
Wavefronts
Physics 102: Lecture 14, Slide 21
ACT: Doppler Practice
V = 32 m/s V = 50 m/s
In the jeep, the frequency of the light from the troopers car will appear:
(1) higher (more blue) (2) Lower (more red)
What value should you use for u in the equation?
(1) 32 (2) 50 (3) 50+32 (4) 50-32