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

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

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

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

Characteristics x S z 11/11/2018

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

Example of a Plane Wave http://pages.vassar.edu/magnes/files/2015/04/planeWave.jpg http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/images/07-EB_Light_320.jpg http://www.seos-project.eu/modules/earthspectra/images/Linear.gif http://www.acs.psu.edu/drussell/Demos/EvanescentWaves/plane-x.gif http://www.acs.psu.edu/drussell/Demos/EvanescentWaves/plane-x.gif 11/11/2018

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

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

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

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

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

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

TM Example 30-4 11/11/2018

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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

Tail of a Comet 11/11/2018

Solar Sail: http://www.lifeslittlemysteries.com/how-do-solar-sails-work--0788/

Solar Sail http://www.popularmechanics.com/cm/popularmechanics/images/Cv/starship-troopers-05-1011-xln-45969457.jpg http://www.popularmechanics.com/science/space/news/solar-sails-fly-from-science-fiction-into-reality#slide-1 11/11/2018

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

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

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

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

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

Emission, Absorption, Scattering 11/11/2018

Photon Range Sensitivity of the Eye 11/11/2018

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

Ruby Laser Energy Levels 11/11/2018