Transcript PPT

Exam 2 next Monday!
• Lecture material
– Magnetism (Lect. 8) – AC circuits (Lect. 13)
– Plus little bit on resonance today (Lect. 14)
• Discussion/HW material
– Discussion 4 – 7 & HW 4 – 7
• Sign up for conflict exams by Thursday!
[email protected]
• Review session Sunday, March 13, 3pm, 141 Loomis
– Will review HE2 from Fall ‘10
• Daylight Savings starts March 13!!!
Physics 102: Lecture 14, Slide 1
Physics 102: Lecture 14
Electromagnetic Waves
Physics 102: Lecture 14, Slide 2
Review: Phasors & Resonance
• At resonance
–
–
–
–
ImaxXL
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
f
ImaxR
– XC > XL Vgen lags I
• At higher frequencies
– XC < XL Vgen lead I
Physics 102: Lecture 14, Slide 3
ImaxXC
Imax(XL-XC)
Preflight 14.1
L
R
As the frequency of the circuit is either raised
above or lowered below the resonant
frequency, the impedance of the circuit:
C
48% Always increases
Resonance in AC Circuits
Only increases for lowering
27% the frequency
Only increases for raising
25% the frequency
Z is minimum at fo!
Z
f0
frequency
Any other frequency will have higher Z!
Physics 102: Lecture 14, Slide 4
Preflight 14.3
At the resonant frequency, which of the
following is true?
9%
I leads Vgenerator
VL
11% I lags Vgenerator
80% I is in phase with Vgenerator
At resonance, VL,max = VC,max, so f = 0.
Vgen is in phase with VR!
f=0
VR
VC
VR is always in phase with I so Vgen is also!
Physics 102: Lecture 14, Slide 5
What is it good for?
L
R
• Current through circuit depends on
frequency (maximum at resonance
frequency fo)
C
– Radio receiver – Picks out radio station freq fo
– Stereo equalizer – Picks out music freq fo
– Picks out signal from protons at fo
– NMR/MRI
Physics 102: Lecture 14, Slide 6
Resonance in Radios
An AC circuit with R= 2 W, L = 0.30 mH 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?
𝑓0 =
L
R
C
1
2𝜋 𝐿𝐶
1
1
12
=
=
9
.
1

10
F
C=
2
2
2f 0  L 2  96.1106   0.30 106
Physics 102: Lecture 14, Slide 7
ACT: Radios
Your 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
𝑓0 =
1
2𝜋 𝐿𝐶
Higher frequency needs smaller capacitor so it can
develop voltage quicker.
Physics 102: Lecture 14, Slide 8
James Clerk Maxwell
(1831-1879)
4 laws unify electricity & magnetism:
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)
Physics 102: Lecture 14, Slide 9
Electromagnetic waves!
Radio antenna
Generator creates oscillating current up and down metal rods
y
I
+
This is an electric dipole!
This is called an electric dipole antenna
Physics 102: Lecture 14, Slide 10
x
Oscillating E field
Electric dipole antenna creates an oscillating electric field
In which direction does the E-field point at this time? ... and now?
NOT QUITE! E-fields do NOT appear everywhere in
space instantaneously, they travel at a finite speed c
Physics 102: Lecture 14, Slide 11
Electromagnetic radiation
• E-fields do NOT appear everywhere in space
instantaneously, they travel at a finite speed c
cT = l
y
x
c
c
EM wave!
t=T
t=0 (one full period) = 1/f
Electric dipole radiation
Physics 102: Lecture 14, Slide 12
c = lf
ACT: EM Waves
Which 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
Alternating E field
moves charges up and
down thru antenna!
Physics 102: Lecture 14, Slide 13
demo
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
y
I
x
EM wave!
E and B fields propagate together as EM waves
Physics 102: Lecture 14, Slide 14
c = lf
Speed of EM wave in vacuum
Recall fundamental constants of electricity and magnetism:
𝜀0 = 8.85 × 10−12 𝐶 2 /𝑁𝑚2
“Permittivity of free space” (electricity)
𝜇0 = 4𝜋 × 10−7 𝑇𝑚/𝐴
“Permeability of free space” (magnetism)
Now multiply them:
2
𝐶
𝑇𝑚𝑁𝑚
−12
−7
𝜀0 𝜇0 = 8.85 × 10
× 4𝜋 × 10
2
𝐶𝑚/𝑠
𝐶/𝑠
𝑁𝑚
𝐴
2
𝑠
= 1.11 × 10−17 2
Note:
𝑚
c=
1
𝜀0 𝜇0
= 3.0 × 108 𝑚/𝑠
Physics 102: Lecture 14, Slide 15
1T = 1 N/Cm/s (from F = qvBsin(θ))
1A = 1 C/s (from I = ΔQ/Δt)
Electromagnetic Waves
y
x
• 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/l = c/l
Physics 102: Lecture 14, Slide 16
Period: T = 1/f
Preflight 14.6 – 14.12
Which of the following are transverse
waves?

•
sound
• light

All but sound!
• 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 = lf
ROYGBIV
Physics 102: Lecture 14, Slide 18
EM Waves Practice
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?
Perpendicular to E, v: Into/out of the page
(2) Label the two tic marks on the x axis (in meters).
E
x
3.1
Physics 102: Lecture 14, Slide 19
6.2
v 3 108 m / s
l= =
= 3.1m
6
f 96.110 / s
Representing EM wave: Wavefronts
This picture only represents EM wave along one line (x-axis)
Imagine a slice in y-z plane
y
E
B
y
z
B
E
z
E-field & B-field same
everywhere along plane
l
Wavefronts – surfaces at crests of EM wave
Physics 102: Lecture 14, Slide 20
x
Doppler Effect
Now the car is moving to the left.
Observed wavelength lo different!
A police car emits light of
wavelength le
Wavefronts
le
l o < le
lo > l e
u
Moving toward observer: fo = fe(1 + u/c)
Moving away from observer: fo = fe(1 – u/c)
Physics 102: Lecture 14, Slide 21
l = c/f
Only relative velocity matters:
u = v1 + v2
moving in opposite directions
u = v1 – v2
moving in same direction
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)
Cars are getting closer together: fo = fe (1 + u/c)
What value should you use for u in the equation?
(1) 32
(2) 50
(3) 50+32
(4) 50-32
Cars are moving in same directions: u = v1 – v2
Physics 102: Lecture 14, Slide 22
See you Wednesday!
Physics 102: Lecture 14, Slide 23