1. How is B related to E? We derived the wave equation for Ex:
We could have derived for By:
How are Ex and By related in phase and magnitude?
Consider the harmonic solution:
where
11/11/2018

2. E & B in Electromagnetic Waves
Plane Wave:
where: x z y
The direction of propagation is given by the cross product
where are the unit vectors in the (E,B) directions.
Nothing special about (Ex,By); eg could have (Ey, -Bx)
Note cyclical relation:
11/11/2018

3. Energy in Electromagnetic Waves
Electromagnetic waves contain energy. We know the energy density stored in E and B fields:
In an EM wave, B = E/c
The total energy density in an EM wave = u, where
The Intensity of a wave is defined as the average power (Pav=uav/t) transmitted per unit area = average energy density times wave velocity:
For ease in calculation define Z0 as:
11/11/2018

4. The Poynting Vector
The direction of the propagation of the electromagnetic wave is given by:
This energy transport is defined by the Poynting vector S as:
S has the direction of propagation of the wave
The magnitude of S is directly related to the energy being transported by the wave
The intensity for harmonic waves is then given by:
11/11/2018

5. Characteristics x S z
11/11/2018

6. Summary of Electromagnetic Radiation
combined Faraday’s Law and Ampere’s Law
time varying B-field induces E-field
time varying E-field induces B-field
E-field and B-field are perpendicular
energy density
Poynting Vector describes power flow
units: watts/m2 E B S
11/11/2018

7. Example of a Plane Wave
11/11/2018

8. QUIZ lecture 21
An electromagnetic plane-wave is traveling in the +z direction. The figure above shows this wave at some instant in time. Points A, B and C have the same z coordinate. Compare the magnitudes of the electric field at points A, B and C.
EA < EC< EB (B) EC < EA< EB
(C) EC = EA< EB (D) EA = EB = EC
(E) EC = EA> EB
11/11/2018

9. At (x,y,z) at time t, what is By?
Consider a point (x,y,z) at time t when Ex is negative and has its maximum value.
At (x,y,z) at time t, what is By?
A) By is positive and has its maximum value
B) By is negative and has its maximum value
C) By is zero
D) We do not have enough information
11/11/2018

10. LECTURE 22
EM wave Intensity I, pressure P, energy density uav from chapter 30
Light wave or particle

11. Dependence of Intensity on Distance
Consider spheres at different radius from the source emitting the EM radiation
power Pav
11/11/2018

12. Transfer of Momentum Total Absorption Total Reflection
Pressure P = F/A, so
11/11/2018

13. TM Example 30-4
A light bulb emits EM waves isotropically. For a distance of 3 m from the light bulb, find (a) the intensity, (b) the radiation pressure, and (c) the electric and magnetic field amplitudes, assuming that 50 W of EM radiation is emitted.
TM comments that ~ 2% of the power consumed is transformed into visible light. Most of the power goes into heat, so this may be a 1000 W bulb.
11/11/2018

14. TM Example 30-4
11/11/2018

15. 11/11/2018

16. Tail of a Comet
A spherical dust particle of density  is released from a comet. What radius R must it have in order for the gravitational force Fg from the sun to balance the sun’s radiation force Fr?
Assume:
1. The Sun is far away & acts as an isotropic light source.
PR is radially outward and FR is radially outward.
FG is directed radially inward.
The particle is totally absorbing.
Ps = 3.9 x1026 W
G=6.67 x10-11 Nm2/kg
Ms=1.99 x 1030 kg
 = 3,500 kg/m3
11/11/2018

17. Tail of a Comet
11/11/2018

18. Solar Sail:

19. Solar Sail
11/11/2018

20. the radiation pressure increases radiation pressure stays the same
Question
Light of uniform intensity shines perpendicularly on a totally absorbing surface, fully illuminating the surface. If the area of the surface is increased:
the radiation pressure increases
radiation pressure stays the same
the radiation pressure decreases.
Radiation Pressure stays the same
Radiation force increases
P=I/c=F/A
F=IA/c
11/11/2018

21. the radiation force increases radiation force stays the same
Quiz lecture 22
Light of uniform intensity shines perpendicularly on a totally absorbing surface, fully illuminating the surface. If the area of the surface is increased:
the radiation force increases
radiation force stays the same
the radiation force decreases.
Radiation Pressure stays the same
Radiation force decreases
11/11/2018

22. Wave-Particle Duality
Isaac Newton (1642–1727): Light is a stream of particles.
Christian Huygen (1629–1695): Light is a wave.
Thomas Young (1801): experimental proof that light is a wave by showing that light exhibits interference phenomena
Augustin Fresnel (1819): submitted a paper on the wave theory of light to explain diffraction to the French Academy of Sciences. If correct, there should be a “Fresnel bright spot”. An Academy test of this showed its existence.
James Clerk Maxwell (1860): wave theory of light
Albert Einstein (1905): particle nature of light to explain the photoelectric effect
11/11/2018

23. Photo-Electric Effect
Observation:
Current does not depend on light intensity
Depend on the wavelength of light
Einstein’s hypothesis:
Photon has energy E=hf=hc/ where h is the Planck’s constant (wave-particle duality)
To release an electron from a metal plate E(photon)> threshold energy
11/11/2018

24. Wave-Particle Duality
Light & Matter can exhibit properties of both waves and particles.
11/11/2018

25. Emission, Absorption, Scattering
11/11/2018

26. Photon Range Sensitivity of the Eye
11/11/2018

27. Laser (Light Amplification by stimulated emission
Ruby is an aluminum oxide crystal in which some Al atoms have been replaced with chromium. Chromium atoms absorb green and blue light and emit or reflect only red light.
11/11/2018

28. Ruby Laser Energy Levels
11/11/2018