1. PHY 102: Lecture 8 8.1 Creating Electromagnetic Wave 8.2 Electromagnetic Spectrum 8.3 Energy of Electromagnetic Wave 8.4 Polarization

2. PHY 102: Lecture 8 Electromagnetic Waves 8.1 Creating Electromagnetic Wave

3. James Clerk Maxwell (1831 – 1879) Scottish Physicist Showed that electric and magnetic fields fluctuating together can form a propagating electromagnetic wave

4. Creating Electric Field - 1 One way to create EM wave Two straight metal wires connected to the terminals of an ac generator Serve as an antenna Potential difference between the terminals changes sinusoidally with time t and has a period T

5. Creating Electric Field Wave - 2 (a) Instant t = 0 s There is no charge at the ends of either wire No electric field at P just to right of antenna

6. Creating Electric Field Wave - 3 (b) Time passes Top wire becomes “+” charged Bottom wire becomes “-” charged t = ¼ T (one quarter cycle) Charges reach maximum values The corresponding electric field E at point P is the red arrow E increased to maximum strength in downward direction Electric fields produced earlier have moved to the right

7. Creating Electric Field Wave - 4 (c) – (e) Show the creation of the electric field at point P (red arrow) at later times during the generator cycle (d) Shows the charges on the wires when the polarity of the generator has reversed The electric field at P has reversed its direction and points upward

8. Creating Electric Field Wave - 5 (e) A complete sine wave has been drawn through the tips of the electric field vectors At distant points, the electric field of the charges is not felt immediately The field is created first near the wire and then, like the effect of a pebble dropped into a pond, moves outward as a wave in all directions

9. Creating Magnetic Field Wave Along with the electric field, a magnetic field B is also created, because the charges flowing in the antenna constitute an electric current, which produces a magnetic field

10. Creating Electromagnetic Wave Magnetic field is perpendicular to the page Electric field lies in the plane of the page The electric and magnetic fields created by the antenna are mutually perpendicular and remains so as they move outward Both fields are perpendicular to the direction of travel These perpendicular electric and magnetic fields, moving together, constitute an electromagnetic wave

11. Electromagnetic Wave The electric and magnetic fields decrease to zero rapidly with increasing distance from the antenna Therefore, they exist mainly near the antenna and together are called the near field Electric and magnetic fields do form a wave at large distance from the antenna These fields arise from an effect that is different from that which produces the near field and are referred to as the radiation field.

12. Speed of Electromagnetic Wave All electromagnetic waves move through a vacuum at the same speed Symbol c is used to denote this speed c = 3.00 x 10 8 m/s In general, they move through a substance such as glass at a speed that is substantially less than c

13. PHY 102: Lecture 8 Electromagnetic Waves 8.2 Electromagnetic Spectrum

14. Electromagnetic Spectrum

15. Spectrum RadiationFrequency (Hz) Wavelength (m) Gamma Rays > 3 x 10 19 < 1 x 10 -12 X Rays 3 x 10 19 - 3 x 10 16 1 x 10 -11 to 1 x 10 -8 Ultraviolet 3 x 10 16 - 7.9 x 10 14 1 x 10 -8 to 3.8 x 10 -7 Visible Light 7.9 x 10 14 - 4 x 10 14 3.8 x 10 -7 to 7.5 x 10 -7 Infrared 4 x 10 14 - 3 x 10 11 7.5 x 10 -7 to 1 x 10 -3 Microwaves 3 x 10 11 - 3 x 10 8 1 x 10 -3 to 1 Radio Waves 3 x 10 8 - 31 to 1 x 10 8

16. Visible Light Spectrum

17. Visible Light ColorWavelength violet380–450 nm blue450–495 nm green495–570 nm yellow570–590 nm orange590–620 nm red620–750 nm

18. PHY 102: Lecture 8 Electromagnetic Waves 8.3 Energy of Electromagnetic Wave

19. Energy Density at Instant of Time Electric energy / Volume = ½  0 E 2 Magnetic energy / Volume = (½  0 )B 2 u = Total energy / Volume u = ½  0 E 2 + (½  0 )B 2 In an electromagnetic wave in vacuum or air, the electric and magnetic field carry equal amount of energy per unit volume u =  0 E 2 u = (1/  0 )B 2

20. Relation between E and B u =  0 E 2 u = (1/  0 )B 2   0 E 2 = (1/  0 )B 2  E 2 = (1/  0  0 )B 2 c 2 = (1/  0  0 ) E = cB

21. Average Energy Density E rms = [1/sqrt(2)]E 0 B rms = [1/sqrt(2)]B 0 E 0 and B 0 are the maximum values of the sinusoidal E and B fields average u =  0 E 2 rms average u = (1/  0 )B 2 rms

22. Problem 1 - 1 Sunlight enters the top of the earth’s atmosphere with an electric field whose rms value is E rms = 720 N/C (a) Find the average total energy density of this wave (b) Find the rms value of the sunlight’s magnetic field

23. Problem 1 - 2 (a) average u =  0 E 2 rms average u = (8.85 x 10 -12 )(720) 2 average u = 4.6 x 10 -6 J/m 3 (b) B rms = E rms /c = 720/3 x 10 8 = 2.4 x 10 -6 T

24. Intensity S = intensity S = P/A = Total energy / tA Total energy = (Total energy density) x vol Total energy = u(ctA) S = Total energy / tA = uctA / tA = cu S = cu = ½ c  0 E 2 + ½ (c/  0 )B 2 S = c  0 E 2 = (c/  0 )B 2 avg S = c  0 E 2 rms

25. PHY 102: Lecture 8 Electromagnetic Waves 8.4 Polarization

26. Polarization of Longitudinal Waves For longitudinal waves the notion of polarization has no meaning

27. Polarized Electromagnetic Waves-1 Electromagnetic waves are transverse waves Transverse waves can be polarized Linearly polarized means that the waves vibration always occurs along one direction This is the direction of polarization

28. Polarized Electromagnetic Waves-2 (a) The direction of polarization is vertical Parallel to the slit Wave passes through (b) Slit is turned perpendicular to direction of polarization Wave cannot pass

29. Polarized Light Waves-3 In an electromagnetic wave, the electric field oscillates along the y- axis The magnetic field oscillates along the z-axis The wave is linearly polarized, with the direction of polarization taken arbitrarily to be that along which the electric field oscillates If the wave is a radio wave generated by a straight-wire antenna, the direction of polarization is determined by the orientation of the antenna

30. Unpolarized Electromagnetic Waves Visible light given off by an incandescent light bulb consists of electromagnetic waves that are completely unpolarized Waves are emitted by a large number of atoms in the hot filament of the bulb When an electron in an atom oscillates, the atom behaves as a miniature antenna that broadcasts light for brief period of time, about 10 -8 s The direction of these atomic antennas changes randomly as a result of collisions Unpolarized light consists of many individual waves, emitted in short bursts by many “atomic antennas”, each with its own direction of polarization

31. Producing Polarized Light Waves-1 Linearly polarized light can be produced from unpolarized light with the aid of certain materials Such materials allow only the component of the electric field along one direction to pass through, while absorbing the field component perpendicular to this direction This is called the transmission axis

32. Producing Polarized Light Waves-2 No matter how transmission axis is oriented, the intensity of the transmitted polarized light is ½ that of the incident unpolarized light

33. Malus’ Law - 1 Produce polarized light with a piece of polarizing material Use a second piece to change the polarization direction and adjust the intensity of the light

34. Malus’ Law - 2 The first piece of polarizing material is called the polarizer The second piece is called the analyzer Transmission axis of the analyzer is at an angle  relative to the transmission axis of the polarizer

35. Malus’ Law - 3 Electric field strength of the polarized light incident on the analyzer is E Field strength passing through is the component parallel to the transmission axis Ecos 

36. Malus’ Law - 4 Intensity is proportional to the square of electric field strength The average intensity of polarized light passing through the analyzer is proportional to cos 2 

37. Malus’ Law average S = average S 0 cos 2  average S 0 is the average intensity of the light entering the analyzer

38. Polarized Light in Nature - 1 Polaroid is a material used in sunglasses The sunglasses are designed so that the transmission axis of the Polaroid is oriented vertically when the glasses are worn in the usual fashion The glasses prevent any light that is polarized horizontally from reaching the eye Light from the sun is unpolarized, but a considerable amount of horizontally polarized sun light originates by reflection from horizontal surfaces such as a lake Polaroid sunglasses reduce glare by preventing the horizontally polarized reflected light from reaching the eyes

39. Polarized Light in Nature - 2 Polarized sunlight also originates from the scattering of light by molecules in the atmosphere The electric fields in the unpolarized sunlight cause the electrons in the molecule to vibrate perpendicular to the direction in which the light travels The electrons reradiate the electromagnetic waves in different directions The light radiated straight ahead is unpolarized But light radiated perpendicular to the incident light is polarized Light radiated in the intermediate direction is partially polarized.