1. Tue. Nov. 11, 2008Physics 208, Lecture 211 From last time… EM waves Inductors in circuits I? + -

2. Tue. Nov. 11, 2008Physics 208, Lecture 212 A Transverse wave. Electric/magnetic fields perpendicular to propagation direction Can travel in empty space f = v/, v = c = 3 x 10 8 m/s (186,000 miles/second)

3. Tue. Nov. 11, 2008Physics 208, Lecture 213 A microwave oven irradiates food with electromagnetic radiation that has a frequency of about 10 10 Hz. The wavelengths of these microwaves are on the order of A. kilometers B. meters C. centimeters D. micrometers Quick Quiz

4. Tue. Nov. 11, 2008Physics 208, Lecture 214 Electromagnetic waves z x y

5. Tue. Nov. 11, 2008Physics 208, Lecture 215 Energy and EM Waves Energy density in E-field Energy density in B-field Total moves w/ EM wave at speed c

6. Tue. Nov. 11, 2008Physics 208, Lecture 216 Power and intensity in EM waves Energy density u E moves at c Instantaneous energy transfer = energy passing plane per second. = This is power density W/m 2 Time average of this is Intensity =

7. Tue. Nov. 11, 2008Physics 208, Lecture 217 Example: E-field in laser pointer 1 mW laser pointer. Beam diameter at board ~ 2mm Intensity = How big is max E-field?

8. Tue. Nov. 11, 2008Physics 208, Lecture 218 Spherical waves Sources often radiate EM wave in all directions Light bulb The sun Radio/tv transmission tower Spherical wave, looks like plane wave far away Intensity decreases with distance Power spread over larger area Source power Spread over this surface area

9. Tue. Nov. 11, 2008Physics 208, Lecture 219 Question A radio station transmits 50kW of power from its antanna. What is the amplitude of the electric field at your radio, 1km away. A.0.1 V/m B.0.5 V/m C.1 V/m D.1.7 V/m E.15 V/m

10. Tue. Nov. 11, 2008Physics 208, Lecture 2110 The Poynting Vector Rate at which energy flows through a unit area perpendicular to direction of wave propagation Instantaneous power per unit area (J/s. m 2 = W/m 2 ) is also Its direction is the direction of propagation of the EM wave This is time dependent Its magnitude varies in time Its magnitude reaches a maximum at the same instant as E and B

11. Tue. Nov. 11, 2008Physics 208, Lecture 2111 Radiation Pressure Saw EM waves carry energy They also have momentum When object absorbs energy U from EM wave: Momentum  p is transferred Result is a force Pressure = Force/Area = ( Will see this later in QM ) Radiation pressure on perfectly absorbing object Power Intensity

12. Tue. Nov. 11, 2008Physics 208, Lecture 2112 Radiation pressure & force EM wave incident on surface exerts a radiation pressure p rad (force/area) proportional to intensity I. Perfectly absorbing (black) surface: Perfectly reflecting (mirror) surface: Resulting force = (radiation pressure) x (area)

13. Tue. Nov. 11, 2008Physics 208, Lecture 2113 Question A perfectly reflecting square solar sail is 107m X 107m. It has a mass of 100kg. It starts from rest near the Earth’s orbit, where the sun’s EM radiation has an intensity of 1300 W/m 2. How fast is it moving after 1 hour? A.100 m/s B.56 m/s C.17 m/s D.3.6 m/s E.0.7 m/s

14. Tue. Nov. 11, 2008Physics 208, Lecture 2114 Polarization of EM waves Usually indicate the polarization direction by indicating only the E-field. Can then be indicated with a line: Unpolarized Plane Polarized x y z Superposition of plane polarized waves

15. Tue. Nov. 11, 2008Physics 208, Lecture 2115 Producing polarized light Polarization by selective absorption: material that transmits waves whose E-field vibrates in a plain parallel to a certain direction and absorbs all others This polarization absorbed This polarization transmitted transmission axis Polaroid sheet Long-chain hydrocarbon molecules Demo on MW and metal grid

16. Tue. Nov. 11, 2008Physics 208, Lecture 2116 Transmission at an angle Incident wave is equivalent to superposition x y transmission  Plane-polarized incident wave polarizer absorbed transmitted Transmitted wave =

17. Tue. Nov. 11, 2008Physics 208, Lecture 2117 Detecting polarized light Polarizer transmits component of E-field parallel to transmission axis absorbs component of E-field perpendicular to transmission axis Transmitted intensity: I = I 0 cos 2  I 0 = intensity of polarized beam on analyzer (Malus’ law) Allowed component parallel to analyzer axis Polaroid sheets

18. Tue. Nov. 11, 2008Physics 208, Lecture 2118 Malus’ law Transmitted amplitude is E o cos  (component of polarization along polarizer axis) Transmitted intensity is I o cos 2  ( square of amplitude) Perpendicular polarizers give zero intensity.

19. Tue. Nov. 11, 2008Physics 208, Lecture 2119 Polarization by reflection Unpolarized Incident light Reflection polarized with E-field parallel to surface Refracted light Unpolarized light reflected from a surface becomes partially polarized Degree of polarization depends on angle of incidence n

20. Tue. Nov. 11, 2008Physics 208, Lecture 2120 Reducing glare Transmission axis Reflected sunlight partially polarized. Horizontal reflective surface ->the E-field vector of reflected light has strong horizontal component.

21. Tue. Nov. 11, 2008Physics 208, Lecture 2121 Circular and elliptical polarization Circularly polarized light is a superposition of two waves with orthogonal linear polarizations, and 90˚ out of phase. The electric field rotates in time with constant magnitude.