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 =