Electromagnetic Waves and Maxwell's Equations

Electromagnetic Waves 1 PHY2054: Chapter 24 (OpenStax)

Chapter 24 Topics 1. Maxwell s equations and electromagnetic waves 2. Production of EM waves 3. The electromagnetic spectrum 4. Energy transport of EM waves 2 PHY2054: Chapter 24 (OpenStax)

Quiz Which of the following has nothing to do with EM waves? (a) Dental x-rays (b) Radio broadcasting (c) Strumming a guitar (d) Cooking a microwave dinner (e) Responding with your HITT transmitter 3 PHY2054: Chapter 24 (OpenStax)

Quiz Which of the following has nothing to do with EM waves? (a) Dental x-rays (b) Radio broadcasting (c) Strumming a guitar (d) Cooking a microwave dinner (e) Responding with your HITT transmitter 4 PHY2054: Chapter 24 (OpenStax)

Electromagnetic Theory First described by Maxwell (1870) Linked the phenomena of electricity and magnetism into a single electromagnetic theory (E&M) Theory described by 4 Maxwell s equations Maxwell s equations (1870) Unified electric fields, electric charges, magnetic fields, electric current into a single theory https://en.wikipedia.org/wiki/Maxwell s_equations 5 PHY2054: Chapter 24 (OpenStax)

Maxwells Equations: Summary 1. Gauss s law for E fields, connects E field over a surface to enclosed electric charge. 2. Gauss s law for B fields, connects B field over a surface to enclosed magnetic charge = 0. 3. Changing B field generates emf to drive a current. Includes Faraday s law and Lenz s law in one equation 4. Describes how a B field is generated by an electric current (Ampere s law) or by a changing E field (new prediction). Major achievement: symmetry of E and B fields in mathematical treatment. 6 PHY2054: Chapter 24 (OpenStax)

Electromagnetism & Unification of Forces Maxwell s equations first example of a unified field theory Unifying several theories and experimental data into a coherent framework (Gauss law, Ampere s law, induction experiments, Faraday s law ) Einstein s quest: unified field theory unifying 4 basic forces Strong force (holds protons-neutrons within nucleus) Weak force (radioactive decay, solar core processes) EM force (via Maxwell) Gravitational force (from Einstein s General Theory of Relativity) www.aps.org/publications/apsnews/200512/history.cfm Einstein s quest still unachieved. But there are some successes Electroweak theory: Unification of weak + EM forces (1970) QCD: explanation of strong force (1970s) String theory: contender for unifying all forces (1980s present) 7 PHY2054: Chapter 24 (OpenStax)

Electromagnetic Waves First described by Maxwell (1870) Proved that electric & magnetic fields would continuously generate one another and propagate as waves through space: Electromagnetic waves Mechanism: E field generates B field, which generates E field, etc. A consequence of Maxwell s equations (requires some math!) EM wave properties: wavelength, frequency, energy, momentum c = l f Predicted velocity from EM constants! 1 m0e0 = 3 108m/s c = 8 PHY2054: Chapter 24 (OpenStax)

Electromagnetic Waves (2) More EM wave tidbits They are generated by accelerated charges (antenna, circular motion, etc) 19th century physicists believed (wrongly, but based on experience) that a substance was needed to carry the waves: Ether Experiments conducted over 40 years failed to detect ether. Einstein banished the idea of an ether in his Special Theory of Relativity (1905) 9 PHY2054: Chapter 24 (OpenStax)

Electromagnetic waves generated by oscillating electrons in dipole antenna. Because the electrons are oscillating up and down, they are accelerating, giving rise to EM radiation. 10 PHY2054: Chapter 24 (OpenStax)

An Electromagnetic Wave hyperphysics.phy-astr.gsu.edu/hbase/electric/imgel2/emwavec.gif See animation at en.wikipedia.org/wiki/Electromagnetic_radiation 11 PHY2054: Chapter 24 (OpenStax)

Electromagnetic Wave Properties 1. Oscillating E and B fields 2. E = Bc (E and B magnitudes are proportional) c =1/ m0e0= 3 108m/s 3. Velocity = c E k 4. E B k (direction of motion) B 5. E x B is in direction of energy intensity vector c = l f 6. Wavelength & frequency 1 1 = 3.00 108m/s c = = ( )4p 10-7 ( ) e0m0 8.85 10-12 12 PHY2054: Chapter 24 (OpenStax)

Direction of E, B, Velocity in E&M Waves 13 PHY2054: Chapter 24 (OpenStax)

Electromagnetic Spectrum Wireless routers use 2.4 or 5 GHz frequencies 14 PHY2054: Chapter 24 (OpenStax)

Solar Spectrum 15 PHY2054: Chapter 24 (OpenStax)

Speed of Light in Matter Speed in matter is always less than c Define index of refraction by v = c / n, with n > 1 Water: n = 1.333 v = 3 108 / 1.333 = 2.25 108 m/s (n varies by substance) Behavior of wavelength and frequency in matter Wavelength: Frequency: fn= f ln= l / n 16 PHY2054: Chapter 24 (OpenStax)

Quiz Which statement is true? The energy carried by an electromagnetic wave in a vacuum (a) propagates at the speed of light (b) consists of only electric field contributions (c) propagates along the direction of the electric field (d) consists of E and B fields pointing in the same direction (e) none of the above 17 PHY2054: Chapter 24 (OpenStax)

Quiz Which statement is true? The energy carried by an electromagnetic wave in a vacuum (a) propagates at the speed of light (b) consists of only electric field contributions (c) propagates along the direction of the electric field (d) consists of E and B fields pointing in the same direction (e) none of the above 18 PHY2054: Chapter 24 (OpenStax)

Reading Quiz A grain of interplanetary dust is in the Sun s gravitational field. Ignoring all non-solar influences, is it possible for the grain to move away from the Sun? (a) Yes, if the grain is sufficiently large (b) Yes, if the grain is sufficiently small (c) No, it cannot escape the Sun s gravitational field 19 PHY2054: Chapter 24 (OpenStax)

Reading Quiz A grain of interplanetary dust is in the Sun s gravitational field. Ignoring all non-solar influences, is it possible for the grain to move away from the Sun? (a) Yes, if the grain is sufficiently large (b) Yes, if the grain is sufficiently small (c) No, it cannot escape the Sun s gravitational field Energy carried by EM wave creates radiation pressure when it strikes an object, with value Pr = I/c, where I is intensity. Solar radiation pressure is important for very small dust grains in the solar system. If the grains are sufficiently small (<150 nm), the total radiation pressure force is larger than gravitational attraction, and the dust grains are blown out of the solar system. 20 PHY2054: Chapter 24 (OpenStax)

Energy Carried by EM Waves Recall energy density of E and B fields B2 m0 2e0E2 uEM= uE+uB uE=1 uB=1 2 uEM= 2uE= 2uB E = Bc makes these equal for EM wave uEM= ce0Erms 2 2 = cBrms / m0 Moving EM wave transports this energy along the wave Add E, B energy contributions, average over period 2 B2 2 E2 Brms Erms Use rms values: 21 PHY2054: Chapter 24 (OpenStax)

Intensity Intensity is related to energy density of moving waves More familiar measure of energy transport (heat from sunlight, etc) Measures power/area of EM waves crossing a surface Units: W/m2 Example: Intensity of 100 W light bulb 5 meters away I = P/ 4pr2=100/ 4p 25 ( )= 0.32W/ m2 Simple to relate intensity to energy density: I = c uT = cBrms 2 2 I = cuEM= ce0Erms m0 Examples on next slides 22 PHY2054: Chapter 24 (OpenStax)

Intensity Example 1 Sunlight is approximately I = 1000 W/m2 at earth surface Find Erms and Brms 1000 )8.85 10-12 I Erms= = = 614 V/m ( ( ) ce0 3 108 Brms=Erms 614 3 108= 2.05 10-6 T = c 23 PHY2054: Chapter 24 (OpenStax)

Intensity Example 2 100 W light bulb. Find quantities at 5 m Find intensity first (as before) 100 I =P P 4 3.14 52= 0.32 W/m2 A= 4pr2= 0.32 )8.85 10-12 I Erms= = =10.9 V/m ( ( ) ce0 3 108 Brms=Erms 10.9 3 108= 3.66 10-8 T = c 24 PHY2054: Chapter 24 (OpenStax)

Radiation Pressure from E&M Waves E&M waves transport energy and momentum Both are consequences of Maxwell s equations Consider beam of radiation striking a surface Energy/time/area = Power / area intensity Momentum/time/area = Force / area radiation pressure PEM = uEM = I / c (radiation pressure in terms of energy density & intensity) Example: 1000 m 1000 m square sail above the atmosphere Find total force for sunlight reflecting 100% from sail Sunlight: I = 1370 W/m2 PEM = 2 4.6 x 10 6 N/m2 (reflection leads to x2 factor) Force = Area PEM = 9.2 N 25 PHY2054: Chapter 24 (OpenStax)

Radiation Pressure: Examples Orbits of earth satellites & space vehicles Measurable corrections to orbits because radiation pressure is steady Clearing small dust particles Dust from early solar system Dust & gas from star clusters Supporting very hot stars from gravitational collapse Small effect for sun Comet tails: radiation pressure + solar wind Solar sails as propulsion mechanism for starships en.wikipedia.org/wiki/Radiation_pressure en.wikipedia.org/wiki/Solar_sail 26 PHY2054: Chapter 24 (OpenStax)

Doppler Effect 27 PHY2054: Chapter 24 (OpenStax)

Doppler Effect Familiar concept with sound, e.g. emergency vehicle siren Siren approaching: frequency increases (wavelength decreases) Siren receding: frequency decreases (wavelength increases) http://www.geography.hunter.cuny.edu/tbw/wc.notes/10.thunderstorms.tornadoes/doppler_effect.htm 28 PHY2054: Chapter 24 (OpenStax)

Doppler Effect and Light Star/galaxy moving towards earth: increase f Star/galaxy moving away from earth: decrease f 29 PHY2054: Chapter 24 (OpenStax)

Doppler Effect: Quantitative Define following quantities: femit = frequency emitted by star/galaxy fobs = frequency observed on earth vrel = velocity of star/galaxy relative to earth (> 0 if approaching) 1+vrel fobs femit c = 1-vrel c When vrel / c < < 1, we can approximate this by fobs femit 1+vrel c 30 PHY2054: Chapter 24 (OpenStax)

Tracking Flight MH370 by Doppler (2014) Stationary satellite (24 hour orbit) Doppler effect depends only on velocity along line of sight Plane v = 540 mi/hr ~240 m/s 80 m/s along line of sight? Df f f =5GHz Df ~1300Hz =v c~ 2.7 10-7 31 PHY2054: Chapter 24 (OpenStax)

Doppler Effect in Astronomy Use Doppler effect and shift in wavelength of spectral lines to measure velocity of star/galaxy. Extremely accurate (measure to a few cm/sec in some cases) The increasing red-shift vs galactic distance is the fundamental basis for knowing that the universe is expanding from a single time. Big bang! vrel= 0 vrel<0 vrel>0 32 PHY2054: Chapter 24 (OpenStax)

Doppler Effect in Astronomy For small velocities lobs lemit fobs femit 1+vrel 1-vrel c c Assume that = 91.2 nm (Lyman alpha line) from a distant galaxy is measured to be 95.6 nm. Find velocity. lobs lemit c =1.0482 =1-vrel vrel= -0.0482c = -15,500km/sec Receding from us 33 PHY2054: Chapter 24 (OpenStax)