1. Lecture 34: MON 13 APR Ch.33.1–3,5–7: E&M Waves
Physics 2102
Jonathan Dowling
James Clerk Maxwell ( )
Lecture 34: MON 13 APR Ch.33.1–3,5–7: E&M Waves

2. MT03 Avg: 65/100
Q1/P3 K. Schafer Office hours: MW 1:30-2:30 pm 222B Nicholson
P1/Q2 J. Dowling Office hours: MWF 10:30-11:30 am 453 Nicholson
P2/Q3 M. Gaarde Office hours: TTh 2:30-3:30 pm 215B Nicholson
P3/Q2 C. Buth Office hours: MF 2:30-3:30 pm 222A Nicholson
A: B: C: D: 50-59

3. Right Hand Rule & Vector Addition!
Right Hand Rule & BI>BII Since I is Closer!

4. Maxwell, Waves and Light
A solution to the Maxwell equations in empty space is
a “traveling wave”…
electric and magnetic “forces” can travel!
The “electric” waves travel
at the speed of light!
Light itself is a wave of
electricity and magnetism!

5. Electromagnetic Waves
A solution to Maxwell’s equations in free space:
Visible light, infrared, ultraviolet,
radio waves, X rays, Gamma
rays are all electromagnetic waves.

8. Radio waves are reflected by the layer of the Earth’s atmosphere called the ionosphere.
This allows for transmission between two points which are far from each other on the globe, despite the curvature of the earth.
Marconi’s experiment discovered the ionosphere! Experts thought he was crazy and this would never work.

9. Maxwell’s Rainbow
The wavelength/frequency range in which electromagnetic (EM) waves (light) are visible is only a tiny fraction of the entire electromagnetic spectrum.
Fig. 33-2
Fig. 33-1
(33-2)

10. The Traveling Electromagnetic (EM) Wave, Qualitatively
An LC oscillator causes currents to flow sinusoidally, which in turn produces oscillating electric and magnetic fields, which then propagate through space as EM waves.
Fig. 33-3
Next slide
Oscillation Frequency:
(33-3)

11. Mathematical Description of Traveling EM Waves
Electric Field:
Wave Speed:
Magnetic Field:
All EM waves travel a c in vacuum
Fig. 33-5
Wavenumber:
EM Wave Simulation
Frequency:
Vacuum Permittivity:
Vacuum Permeability:
Amplitude Ratio:
Magnitude Ratio:
(33-5)

12. The Poynting Vector: Points in Direction of Power Flow
Electromagnetic waves are able to transport energy from transmitter
to receiver (example: from the Sun to our skin).
The power transported by the wave and its
direction is quantified by the Poynting vector.
John Henry Poynting ( )
For a wave, since
E is perpendicular to B:
Units: Watt/m2
In a wave, the fields change with time. Therefore the Poynting vector changes too!!
The direction is constant, but the magnitude changes from 0 to a maximum value. E B S

13. EM Wave Intensity, Energy Density
A better measure of the amount of energy in an EM wave is obtained by averaging the Poynting vector over one wave cycle.
The resulting quantity is called intensity. Units are also Watts/m2.
The average of sin2 over
one cycle is ½:
or,
Both fields have the
same energy density.
The total EM energy density is then

14. Solar Energy
The light from the sun has an intensity of about 1kW/m2. What would be the total power incident on a roof of dimensions 8m x 20m ?
I = 1kW/m2 is power per unit area.
P = IA = (103 W/m2) x 8m x 20m = 0.16 MegaWatt! !
The solar panel shown (BP-275) has dimensions 47in x 29in. The incident power is then 880 W. The actual solar panel delivers 75W (4.45A at 17V): less than 10% efficiency….
The electric meter on a solar home runs backwards — Entergy Pays YOU!

15. EM Spherical Waves
The intensity of a wave is power per unit area. If one has a source that emits isotropically (equally in all directions) the power emitted by the source pierces a larger and larger sphere as the wave travels outwards: 1/r2 Law!
So the power per unit area decreases as the inverse of distance squared.

16. Example
A radio station transmits a 10 kW signal at a frequency of 100 MHz. At a distance of 1km from the antenna, find the amplitude of the electric and magnetic field strengths, and the energy incident normally on a square plate of side 10cm in 5 minutes.
Received
energy:

17. Radiation Pressure F [N/m2]
Waves not only carry energy but also momentum. The effect is
very small (we don’t ordinarily feel pressure from light). If light
is completely absorbed during an interval Dt, the momentum
transferred is given by F
and twice as much if reflected. A
Newton’s law: I
Now, supposing one has a wave that hits a surface
of area A (perpendicularly), the amount of energy
transferred to that surface in time Dt will be
therefore
Radiation pressure:
[N/m2]

18. Radiation Pressure & Comet Tails

19. Solar Sails: Photons Propel Spacecraft!
StarTrek DS9
NASA Concept
NASA Demo

20. EM waves: polarization
Radio transmitter:
If the dipole antenna
is vertical, so will be
the electric fields. The
magnetic field will be
horizontal.
The radio wave generated is said to be “polarized”.
In general light sources produce “unpolarized waves”emitted by atomic motions in random directions.

21. EM Waves: Polarization
Completely unpolarized light will have
equal components in horizontal and vertical
directions. Therefore running the light through
a polarizer will cut the intensity in half: I=I0/2
When polarized light hits a polarizing sheet,
only the component of the field aligned with the
sheet will get through.
And therefore:

22. Example
Initially unpolarized light of intensity I0 is sent into a system of three polarizers as shown. What fraction of the initial intensity emerges from the system? What is the polarization of the exiting light?
Through the first polarizer: unpolarized to polarized, so I1=½I0.
Into the second polarizer, the light is now vertically polarized. Then, I2 = I1cos260o = 1/4 I1 = 1/8 I0.
Now the light is again polarized, but at 60o. The last polarizer is horizontal, so I3 = I2cos230o = 3/4 I2 =3 /32 I0 = I0.
The exiting light is horizontally polarized, and has 9% of the original amplitude.