1. Physics 102: Lecture 14, Slide 1
Electromagnetic Waves
Physics 102: Lecture 14

2. 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
Vgen,max
φ

3. Physics 102: Lecture 14, Slide 3
Preflight 14.1
As the frequency of the circuit is either raised
above or lowered below the resonant
frequency, the impedance of the circuit:
Always increases
Resonance in AC Circuits
frequency
Only increases for lowering
the frequency
Only increases for raising
the frequency
f0
Z
L
R
C

4. Physics 102: Lecture 14, Slide 4
Preflight 14.3
At 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
φ = 0

5. 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
L
R
C

6. Physics 102: Lecture 14, Slide 6
Resonance in Radios
An AC circuit with R= 2 Ω, L = 0.30 µH 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?
L
R
C

7. 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

8. 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!

9. Physics 102: Lecture 14, Slide 9
Radio antenna
Generator creates oscillating current up and down metal rods
+
-
I
x
y
This is called an electric dipole antenna
This is an electric dipole!

10. Physics 102: Lecture 14, Slide 10
Oscillating E field
Electric 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?

11. 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 = λ
c = λf
cc
EM wave!

12. Physics 102: Lecture 14, Slide 12
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
demo

13. 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 = λf
E and B fields propagate together as EM waves
II

14. Physics 102: Lecture 14, Slide 14
�0 = 4� × 10−7
𝑇�/�
Recall fundamental constants of electricity and magnetism:
“Permeability of free space” (magnetism)
�0 = 8.85 × 10−12
�2
/��2
“Permittivity of free space” (electricity)
�0�0 = 8.85 × 10−12
�2
��2
× 4� × 10−7
𝑇�
�
Speed of EM wave in vacuum
Now multiply them:
�0�0 = 8.85 × 10−12
�2
��2
× 4� × 10−7
��
��/� �/�
= 1.11 × 10−17
�2
�2 Note:
1T = 1 N/Cm/s (from F = qvBsin(θ))
1A = 1 C/s (from I = ΔQ/Δt)1
ඥ�0�0
= 3.0 × 108
�/�c =

15. Physics 102: Lecture 14, Slide 15
Electromagnetic Waves
x
z
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

16. 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)

17. Physics 102: Lecture 14, Slide 17
Electromagnetic Spectrum
• Light, Radio, TV, Microwaves, X-Rays are
all electromagnetic waves!
c = λf
R O Y G B I V

18. 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

19. Physics 102: Lecture 14, Slide 19
This picture only represents EM wave along one line (x-axis)
x
z
y
Representing EM wave: Wavefronts
Imagine a slice in y-z plane
y
z
E-field & B-field same
everywhere along plane
λ
Wavefronts – surfaces at crests of EM wave

20. Physics 102: Lecture 14, Slide 20
Doppler Effect
Now the car is moving to the left.
Observed wavelength λo different!
u
A police car emits light of
wavelength λe
λe λo < λe λo > λe
Moving toward observer: fo = fe(1 + u/c)
Only relative velocity matters:
u = v1 + v2 moving in opposite directions
u = v – v moving in same direction
λ = f/cMoving away from observer: fo = fe(1 – u/c)
Wavefronts

21. 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