Physics 1425: General Physics I

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Electromagnetic Waves andPolarizationPhysics 2415 Lecture 30Michael Fowler UVa Today s Topics.
Measuring the speed of light Wave energy and power the Poynting vector Light momentum and radiation pressure Radio transmission Polarization.
First Measurement of the Speed of LightRoemer in 1676 noticed that eclipses of Jupiter s satellite Iogradually fell behind a regular schedule for about half the year then just as gradually caught back up He figured it was because the Earth was going away from Jupiter.
for a little over half a year then approaching again it s a Dopplereffect He got a reasonable estimate of the speed of light First Measurement on EarthLight goes out between teeth of rotating wheel reflects off distant mirror by the time it gets back a tooth may be blocking its path depending on.
wheel speed at certain speeds the observer sees nothing Knowing thewheel rotation rate the speed of light can be figured out 1849 720 teeth Best Early Measurements of the Speed ofLight 1879 .
were by a physics instructor Albert Michelson atthe Naval College in Annapolis his rich father in law who had a castle in Scarsdale bankrolledthe experiment It was within about 50 km sec The velocity of light c is precisely .
c 2 99792458 x 108 m sec This is exact because it s the definition of themeter The second is defined as a precisenumber of oscillations of a particular atom Speed of Light.
The speed of light is2 Center of the Earth2 99792458x108 m sec3 Center of the Sunrelative to 4 Center of the Universe.
5 All of the above Speed of LightThe speed of light is2 Center of the Earth2 99792458x108 m sec.
3 Center of the Sunrelative to 4 Center of the Universe5 All of the aboveThat s the Theory of Special Relativity but it s not in this course so you ll all get three points .
Wave Energy Recall we found the energy meter in avibrating string then multiplying that by thewave speed gave power delivered by the wave The same analysis works for electromagnetic.
waves for a harmonic wave E E0 sin kx t and from the previous lecture E vB cB The energy density u E B mean rms values isu 0 E B 0 0 E c 0 EB using B E c c 1 0 0 to see magnetic energy electric .
Wave Power The energy density in the harmonic wave isequal to u c 0 EB joules m3 c 1 0 0 The power intensity the energy deliveredacross one square meter perpendicular to the.
direction of the wave equals the energy in avolume with a base of 1 sq m a length of c 3x108 meters Intensity S cu c 0 E 2 c 2 0 EB EB 0 These terms all represent power m2 in watts .
Poynting Vector The energy density in the harmonic wave isequal to u c 0 EB joules m3 Intensity power delivery m2 is S EB 0 Obviously this power is delivered in a.
particular direction that of the wave and canbe represented as a vector S 1 0 E B This is called the Poynting vector .
Poynting Vector for Static Fields The Poynting vector gives energy I1flow even for static fields If an electric field E is driving asteady current I along a wire there.
will be a magnetic field B 0I 2 r and so a Poynting flow S E B 0inwards as shown here Flow across a cylindrical surface ofradius r length 1 meter will be .
AEB 0 A area 2 r so total Eenergy flow rate EI This is justEnergy flows out of the battery the power dissipated as heat through space down into the wire Light has Momentum.
Maxwell proved from his equations that a flashof light with total energy E carries momentum The proof is quite difficult but one way to seethe result is to use Einstein s equation E mc2 The energy E in a flash of a beam of light.
means it has a very tiny mass E c2 moving ofcourse at c so momentum p mv mc E c All you need to know is the result Radiation Pressure Since light carries momentum anything.
absorbing or reflecting light feels a pressure aforce equal to the rate of change ofmomentum from Newton s laws How can the perpendicular E and B fieldspush something forwards .
The electric field causes charged particles electrons to oscillate perpendicular to thewave direction then the force qv B from themagnetic field pushes the charge forwards Radiation Pressure.
The equation p E c means that it takes a lotof energy to get much momentum The only known successful antisatellite laser called MIRACL delivered one megawattcontinuous power to an area of 200cm2 .
If all that energy hits a satellite veryapproximately what force does it exert A 100N B 10N C 1N D 0 1N E 0 01N Radiation Pressure If one megawatt hits a satellite very.
approximately what force does it exert E 0 01N approximately p E c means 1 Mw or 106J sec is momentum 106 3x108 3x10 3delivered per second and force is rate ofchange of momentum so this is 3x10 3N If.
the radiation is reflected the force is doubleThe point is to fry the satellite not to push it Radio Transmission The basic radio transmitter is anoscillating dipole at some.
instant a dipole is created itsfield propagates outwards but itrapidly dies to be replaced by adipole in the opposite direction the outgoing electric field.
must switch direction it doesthis by looping around as seenhere The magnetic field linesfrom current up and down thedipole antenna are circular Some animations.
Radio Reception Although the radio wave looks complicatednear the transmitter far away meaning morethan a few wavelengths it has the familiar formshown above the direction of propagation.
being directly away from the source For the wave shown above generated by avertical transmitting antenna reception wouldbe best with a vertical receiving antenna Theoscillating vertical electric field would set up.
oscillating currents in a vertical wire Radio Reception A radio receiving antenna has simultaneouslymany small oscillating currents from all thetransmitters within range .
The antenna is linked to an LC circuit withtuneable oscillation frequency this circuit isdriven by the antenna current with the rightfrequency the signal is then amplified Frequencies vary from kHz to GHz and f c.
gives the corresponding wavelengths Polarization The electromagnetic wave shown above issaid to be vertically polarized meaning thedirection of the electric field vector is.
A wave like this with the electric fieldvector at an angle to the vertical can berepresented as a sum of a vertically polarized wave of amplitude Ecos and ahorizontally polarized wave of amplitude.
Polarizing Light Ordinary light is a random mixture ofpolarizations Certain materials like polaroid only allow light polarized say vertically to These materials have long horizontal.
electrically conducting molecules so thehorizontal component of the electric field isabsorbed driving currents in these molecules How Much Intensity Gets Through Polaroid For a wave polarized at to the.
vertical only the component EEcos gets through This meansthe intensity is down by a factorcos2 For incoming light with random.
polarizations the reduction inintensity will be cos 12 Polarization by Reflection We ll discuss this in more detail later but justmention here that reflected light is partially.
polarized that from a flat horizontal surfacepartially horizontally polarized polaroidsunglasses cut this out Light reflected from a surface between twomaterials with different refractive indices n1 n2.
is fully polarized if reflected at Brewster sangle given by tan p n2 n1 were by a physics instructor, Albert Michelson, at the Naval College in Annapolis—his rich father-in-law (who had a castle in Scarsdale) bankrolled the experiment. (It was within about 50 km/sec.) The velocity of light . c. is precisely: c = 2.99792458 x 108 m/sec. This is . exact, because it’s the definition of the meter. (The . second

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