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Electromagnetic Waves 1 Administrative ◦ Quiz Today ◦ Review Exam Grades ◦ Review Exam Begin Chapter 23 – Electromagnetic Waves No 10:30 Office Hours Today. (Sorry) Next Week … More of the same. Watch for still another MP Assignment ◦ Will they ever stop??? (No) Electromagnetic Waves 2 3 12 10 Section 003 8 Average = 55% 6 4 2 0 <10 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100 Electromagnetic Waves 4 12 10 Section 004 8 Average*52 6 4 2 0 <10 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100 Electromagnetic Waves Electromagnetic Waves 5 What do we learn from this? 6 Some of you studied. Some of you didn’t. If you didn’t, do. Or take my Studio Class in the Spring! Electromagnetic Waves Electric Fields and Potential Magnetic Fields The interactions between E & M E&M Oscillations (AC Circuits/Resonance) James Clerk Maxwell related all of this together is a form called Maxwell’s Equations. Electromagnetic Waves 7 James Clerk Maxwell 1831 – 1879 Electricity and magnetism were originally thought to be unrelated In 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena Electromagnetic theory of light Electromagnetic Waves 8 Maxwell Equations closed surface enclosed charge closed surface no mag. charge closed loop linked flux closed loop linked current + flux • Conservation of energy • Conservation of charge Lorentz force law Electromagnetic Waves 9 When an E or B field is changing in time, a wave is created that travels away at a speed c given by: 1 c 3 108 m / s 0 0 This is the experimental value for the speed of light. This suggested that Light is an Electromagnetic Disturbance, In depth experimental substantiation followed. Electromagnetic Waves 10 Can travel through empty space or through some solid materials. The electric field and the magnetic field are found to be orthogonal to each other and both are orthogonal to the direction of travel of the wave. EM waves of this sort are sinusoidal in nature. ◦ Picture a sine wave traveling through space. Electromagnetic Waves 11 Hertz’s Confirmation of Maxwell’s Predictions 1857 – 1894 First to generate and detect electromagnetic waves in a laboratory setting Showed radio waves could be reflected, refracted and diffracted (later) The unit Hz is named for him Electromagnetic Waves 12 An induction coil is connected to two large spheres forming a capacitor Oscillations are initiated by short voltage pulses The oscillating current (accelerating charges) generates EM waves Several meters away from the transmitter is the receiver ◦ This consisted of a single loop of wire connected to two spheres When the oscillation frequency of the transmitter and receiver matched, energy transfer occurred between them Hertz hypothesized the energy transfer was in the form of waves ◦ These are now known to be electromagnetic waves Hertz confirmed Maxwell’s theory by showing the waves existed and had all the properties of light waves (e.g., reflection, refraction, diffraction) ◦ They had different frequencies and wavelengths which obeyed the relationship v = f λ for waves ◦ v was very close to 3 x 108 m/s, the known speed of light Two rods are connected to an oscillating source, charges oscillate between the rods (a) As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = 0 moves away from the rod (b) The charges and field reverse (c) – the oscillations continue (d) Because the oscillating charges in the rod produce a current, there is also a magnetic field generated As the current changes, the magnetic field spreads out from the antenna The magnetic field is perpendicular to the electric field A changing magnetic field produces an electric field A changing electric field produces a magnetic field These fields are in phase At any point, both fields reach their maximum value at the same time Electromagnetic Waves 19 Electromagnetic Waves 20 Was It Magic? Electromagnetic Waves 21 Electromagnetic Waves 22 • The waves are transverse: electric to magnetic and both to the direction of propagation. •The ratio of electric to magnetic magnitude is E=cB. •The wave(s) travel in vacuum at c. •Unlike other mechanical waves, there is no need for a medium to propagate. The old RH-Rule ◦ turn E into B and you get the direction of propagation c. ◦ Rotate c into E and get B. ◦ Rotate B into c and get E. Electromagnetic Waves 26 l Electromagnetic Waves 27 Electromagnetic Waves 28 Electromagnetic Waves 29 Seeing in the UV, for example, steers insects to pollen that humans could not see. Electromagnetic Waves 30 Electromagnetic Waves 31 Electromagnetic Waves 32 Two types of waves Electromagnetic Waves 33 LikeSound Waves,the equation for a moving EM wave is : t x E E m axSin(2 ) Em axSin(t kx) T l t x B Bm axSin(2 ) Bm axSin(t kx) T l 2 k l Em ax cBm ax c l f Suggestion – Look again at the chapter on sound to solidify this stuff. Electromagnetic Waves 34 V c t How much Energy is in this volume? Electromagnetic Waves 35 Light carries Energy and Momentum Electromagnetic Waves 36 & Electromagnetic Waves 37 Energy 1 1 u 0E 2 B 2 Volume 2 20 From before E cB E E B E 0 0 c 1 0 0 B 2 0 0 E 2 Electromagnetic Waves 38 So. B 2 0 0 E 2 ng Substituti into the previous, 1 1 u 0E 2 0 0 E 2 2 20 or 1 1 u 0E 0E2 0E2 2 2 2 Energy stored in the B and B fields are the same! Electromagnetic Waves 39 • Electric and magnetic fields contain energy, potential energy stored in the field: uE and uB uE: ½ 0 E2 electric field energy density uB: (1/0) B2 magnetic field energy density •The energy is put into the oscillating fields by the sources that generate them. •This energy can then propagate to locations far away, at the velocity of light. Energy per unit volume is B dx u = uE + uB 1 ( 0 E 2 1 B2 ) 2 0 area E A Thus the energy, dU, in a box of area A and length dx is 1 dU ( 0 E 2 1 B2 ) Adx c propagation 2 0 direction Let the length dx equal cdt. Then all of this energy leav the box in time dt. Thus energy flows at the rate dU 1 1 2 ( 0 E 2 B ) Ac dt 2 0 B Rate of energy flow: dx dU c 1 2 ( 0 E 2 B )A dt 2 0 area A E We define the intensity S, as the rate of energy flow per unit area: S c ( E 2 1 B2 ) c propagation 2 0 0 direction Rearranging by substituting E=cB and B=E/c, we get, S c ( cEB 1 EB ) 1 ( c 2 1 )EB EB 2 0 0c 20 0 0 0 B In general, we find: dx S = (1/0) EB area E A S is a vector that points in the direction of propagation of the wave and represents the rate of S propagation energy flow per unit area. direction We call this the “Poynting vector”. Units of S are Jm-2 s-1, or Watts/m2. The Inverse-Square Dependence of S A point source of light, or any radiation, spreads out in all directions: Power, P, flowing through sphere Source is same for any radius. P S 4r 2 Source r Area r 2 1 S 2 r Intensity of light at a distance r is S= P / 4r2 P 1 2 I Erms 4r 2 0 c P0 c ( 250W )( 4 107 H / m )( 3108 m / s ) . Erms 4r 2 4 ( 18m )2 . Erms 48V / m Erms 48V / m B 8m / s 0.16 T c . 310 • When present in large flux, photons can exert measurable force on objects. • Massive photon flux from excimer lasers can slow molecules to a complete stop in a phenomenon called “laser cooling”. Momentum and energy of a wave are related by, p = U / c. Now, Force = d p /dt = (dU/dt)/c pressure (radiation) = Force / unit area P = (dU/dt) / (A c) = S / c Radiation Pressure Prad S c Polarization The direction of polarization of a wave is the direction of the electric field. Most light is randomly polarized, which means it contains a mixture of waves of different polarizations. Ey B Polarization z direction x Polarization A polarizer lets through light of only one polarization: E0 E Transmitted light q has its E in the direction of the polarizer’s transmission axis. E = E0 cosq hence, S = S0 cos2q - Malus’s Law At least of this chapter. Electromagnetic Waves 50