1. PHYSICS 272 Electric & Magnetic Interactions
Lecture 27
(last lecture)
Electromagnetic Waves and Radiation [Chap 24]

2. A Few Reminders Final Exam: 12/16 Thursday 10:20-12:20 STEW 183
Special accommodation students: watch s
Students with conflicts: contact me asap by and indicate if availability on 12/16 Thurs morning
Equation sheet will be provided/posted
There will be recitation and lab this week; the lab will be review with some final practice problems
Grading issues/complaints  bring to TA by next Tues (12/14) and Prof by 12/16

3. Gauss’s law for magnetism
Maxwell’s Equations
Integral form
Differential form
Gauss’s law
Gauss’s law for magnetism
Faraday’s law
Ampere-Maxwell law
+ Lorentz force 3

4. Summary

5. . x 1. The direction of the field is opposite to qa
Radiate outward in
(almost) all directions
B-field . x
B = 0
The derivation* is given in 24.11
1. The direction of the field is opposite to qa
2. The electric field falls off at a rate 1/r

6. Sinusoidal Electromagnetic Radiation
Acceleration:
Sinusoidal E/M field 6

7. Sinusoidal E/M Radiation: Wavelength
Instead of period can
use wavelength:
Freeze picture in time:
Example of sinusoidal E/M radiation:
atoms
radio stations
E/M noise from AC wires 7

8. Sinusoidal electromagnetic radiation
An accelerated charge emits a single brief pulse of electromagnetic radiation
The charge emits continuous radiation if it is moved sinusoidally

9. Energy density in E & M fields:

10. In a time ∆t, a volume
of E & M fields passes through the area A.
The amount of energy is
Define energy flux as J/sec/m2
Define the “Poynting vector”
Its direction is the energy flow direction.

11. Electromagnetic Radiation Carries Momentum
Einstein’s equation:
For E&M radiation:
Define momentum flux is 1/c times the energy flux given by the Pointing vector
The units of momentum flux are the same as pressure
in N/m2

13. Incident radiation
Re-radiation

14. Cardboard Why there is no light going through a cardboard?
Electric fields are not blocked by matter
Electrons and nucleus in cardboard reradiate light
Behind the cardboard reradiated E/M field cancels original field 14

15. Effect of E/M Radiation on Matter
Radiative pressure – too small to be observed in most cases
E/M fields can affect charged particles: nucleus and electrons
(electrons in conductors, insulators, molecules…)
Both fields (E and M) are always present – they ‘feed’ each other
But usually only electric field is considered (B=E/c) 15

16. Interaction is particularly strong if incident radiation “in resonance” with electrons in matter
E/M radiation waves with frequency ~106 Hz has big effect on mobile electrons in the metal of radio antenna:
can tune radio to a single frequency
E/M radiation with frequency ~ 1015 Hz has big effect on organic molecules:
retina in your eye responds to visible light but not radio waves
Organic molecules – electronic system is in resonance with E/M frequencies corresponding to ‘visible’ light
Very high frequency (X-rays) has little effect on atoms and can pass through matter (your body):
X-ray imaging 16

17. Polarized E/M Radiation
AC voltage
(~300 MHz)
E/M radiation can be polarized along one axis… no
light
…and it can be unpolarized:
At every single time E is of course in just one direction, but it changes randomly and rapidly over time
Light from the sun is not polarized!
polarized 17

18. Polarized Light Making polarized light Turning polarization
Polaroid sunglasses and camera filters:
Show trick with three polarizers – two crossed ones, add one at 45 degrees in the middle
Sheet of special plastic whose long molecules are aligned with each other
Sunglasses
reflected light is highly polarized: can block it
Considered: using polarized car lights and polarizers-windshields 18

19. In which of these situations will the bulb light?
None
B and C A 19

20. C 20

21. Why the Sky is Blue Why there is light coming from the sky?
N2,O2
Why is it polarized?
Why is it blue? z A A
Energy flux:
No such effect on moon - black sky even if sun can be seen.
It is polarized – use polaroid sunglasses to check it
Why are distant mountains blueish?
Blue: High frequency
Ratio of blue/red frequency is ~2  scattering intensity ratio is 16
Why is sun red at sunset?
Why are distant mountains blue? 21

22. A Few Reminders Final Exam: 12/16 Thursday 10:20-12:20 STEW 183
Special accommodation students: watch s
Students with conflicts: contact me asap by and indicate if availability on 12/16 Thurs morning
Equation sheet will be provided/posted
There will be recitation and lab this week; the lab will be review with some final practice problems
Grading issues/complaints  bring to TA by next Tues (12/14) and Prof by 12/16