This lecture discusses Maxwell's equations and how they govern the propagation of electromagnetic waves. It covers the Poynting vector, which describes the direction and magnitude of energy transport by electromagnetic fields. Radiation pressure, the momentum transfer from absorbed or reflected light, is also discussed. The document provides examples of these concepts, such as using the Poynting vector to calculate power delivered to a resistor or determining the acceleration of the IKAROS spacecraft from radiation pressure.

1. Lecture 18
• Maxwell’s equations and
electromagnetic waves: propagation
and generation
•Energy transport by electromagnetic
fields: the Poynting vector
•Momentum transfer by absorption or
reflection of light: radiation pressure

2. Midterm #2: Thursday, November 14
• Exam is in Galileo
•8:10-9:25: Arrive early so you can
begin on time
•Cover sheet posted next week.
•Focus on material since Midterm #1:
from magnetic fields and forces to
electromagnetic waves!
•Review/practice in recitations 11/13

3. Closer look: how Faraday’s Law and
Ampère’s Law govern propagation of light:
(Faraday’s Law)
(Ampère’s Law)
http://www.amanogawa.com/archive/PlaneWave/PlaneWave.html

4. Wave equation is linear in EM field:
superpositions of waves are waves, too
Standing waves:
Individual traveling waves have E, B in phase
with each other… but the resulting standing
waves have E, B offset from each other!
http://webphysics.davidson.edu/applets/Superposition/GroupVelocity.html

5. Generation of electromagnetic waves:
accelerating charges
http://webphysics.davidson.edu/applets/retard/Retard_FEL.html

6. Energy transport by electromagnetic fields
Energy density in any region with electric and magnetic fields:
EM traveling wave?
∝
Poynting vector
gives
carried by wave,
and direction that power is being delivered

7. Poynting vector isn’t just for EM waves!
Example: A current i runs through a uniform cylindrical
resistor R with radius a and length . Use the Poynting
vector to find the electromagnetic power delivered to the
resistor.
a
ℓ
i

8. EM waves: time-averaged power and intensity
is
/
/
B
Time-average over many cycles?
“intensity”= Savg =

9. Example: HMC quantum optics pump laser
Example: The pump laser used in the HMC quantum
optics lab is a 50-mW violet diode laser (wavelength
405nm). If it is focused to a circular spot with an
effective diameter of 2mm, what is the intensity of the
light? What is the maximum electric field amplitude?

10. Radiation pressure: momentum transfer on
absorption or reflection of light
is
/
Light carries momentum =
/
Radiation pressure:

11. Example: IKAROS Interplanetary Kite-craft
Accelerated by Radiation Of the Sun
Example: The IKAROS mission (2010-2012) achieved
the first demonstration of radiation pressure propulsion
in interplanetary travel. The IKAROS spacecraft had a
mass of 307kg and a trapezoidal solar sail with a 20m
diagonal, as shown. What acceleration did it achieve due
to radiation pressure?

12. IKAROS attitude control via reflectance control

13. Summary
•Poynting vector
gives power/area
delivered by EM fields
•EM fields of light oscillate fast: usually deal
with time-averaged power and intensity of
light
•Radiation pressure:
Force/area on absorber =
Force/area on reflector =