lecture18 2013
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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
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
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
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
Generation of electromagnetic waves: accelerating charges
http://webphysics.davidson.edu/applets/retard/Retard_FEL.html
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
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 Poyntingvector to find the electromagnetic power delivered to the resistor.
a
ℓ
i
EM waves: time-averaged power and intensity
is / /
Time-average over many cycles?“intensity”= Savg =
B
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?
Radiation pressure: momentum transfer on absorption or reflection of light
is /
Radiation pressure:
Light carries momentum =
/
Example: IKAROS Interplanetary Kite-craft Accelerated by Radiation Of the SunExample: 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?
IKAROS attitude control via reflectance control
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 =
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