Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/3
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1 Physics 201 p. 1/3 Physics 201 Professor P. Q. Hung 311B, Physics Building
2 Physics 201 p. 2/3 What are electromagnetic waves? Electromagnetic waves consist of electric fields and magnetic fields which are mutually perpendicular and also perpendicular to the direction of propagation Electromagnetic waves are transverse waves.
3 Physics 201 p. 2/3 What are electromagnetic waves? Electromagnetic waves consist of electric fields and magnetic fields which are mutually perpendicular and also perpendicular to the direction of propagation Electromagnetic waves are transverse waves. Electromagnetic waves can travel in vacuum or in a material.
4 Physics 201 p. 2/3 What are electromagnetic waves? Electromagnetic waves consist of electric fields and magnetic fields which are mutually perpendicular and also perpendicular to the direction of propagation Electromagnetic waves are transverse waves. Electromagnetic waves can travel in vacuum or in a material. The speed of electromagnetic waves in vacuum is the speed of light in vacuum: c = m/s.
5 Physics 201 p. 3/3 What are electromagnetic waves? Electromagnetic waves can be created by oscillating charges Frequency of electromagnetic waves = frequency of charge oscillation. For example, oscillating electrons in an antenna. More on this below.
6 What are electromagnetic waves? Physics 201 p. 4/3
7 What are electromagnetic waves? Physics 201 p. 5/3
8 What are electromagnetic waves? Physics 201 p. 6/3
9 What are electromagnetic waves? Physics 201 p. 7/3
10 Physics 201 p. 8/3 Maxwell s contribution Recall Faraday s law of induction: changing magnetic flux electric field that changes with time Can a magnetic field be created by a changing electric flux?
11 Physics 201 p. 8/3 Maxwell s contribution Recall Faraday s law of induction: changing magnetic flux electric field that changes with time Can a magnetic field be created by a changing electric flux? Maxwell: Ampere s law is good only for a continuous current. What happens between the two plates of a capacitor? If one were to measure the magnetic field around the gap, one would find out that the magnetic field is non-zero! But where is the current between the gap?
12 Physics 201 p. 9/3 Maxwell s contribution Gauss law: EA = q/ɛ 0 q = ɛ 0 AE I = q t = ɛ 0A E t
13 Physics 201 p. 9/3 Maxwell s contribution Gauss law: EA = q/ɛ 0 q = ɛ 0 AE I = q t = ɛ 0A E t There is a uniform electric field between the plates and assume the surface area of each plate is A. The electric flux through an area A is Φ E = EA.
14 Physics 201 p. 10/3 Maxwell s contribution Maxwell: Imagine a fictitious current which he called a displacement current: Φ I d = ɛ E 0 t = ɛ 0 A E t = I. Add that displacement current to the right-hand-side of Ampere s law changing electric field magnetic field that changes with time. That s Maxwell s contribution Maxwell s equations. Why is it so important?
15 Physics 201 p. 11/3 Maxwell s contribution The solution to Maxwell s equations Electromagnetic waves Speed of the waves in vacuum: c = 1 ɛ0 µ 0 = m/s
16 Physics 201 p. 11/3 Maxwell s contribution The solution to Maxwell s equations Electromagnetic waves Speed of the waves in vacuum: c = 1 ɛ0 µ 0 = m/s Light is an electromagnetic wave!
17 Physics 201 p. 12/3 What is the electromagnetic spectru Accelerating charges Radiation.
18 Physics 201 p. 12/3 What is the electromagnetic spectru Accelerating charges Radiation. Like any wave, there is a relationship between the speed of the wave and the frequency and wavelength. Here v = c in vacuum. c = fλ
19 Physics 201 p. 12/3 What is the electromagnetic spectru Accelerating charges Radiation. Like any wave, there is a relationship between the speed of the wave and the frequency and wavelength. Here v = c in vacuum. c = fλ High frequency Short wavelength and vice versa.
20 Physics 201 p. 13/3 Spectrum Radio waves: λ 10 4 m 0.1m. Generated by electronic devices like an LC oscillator. Used in radio and television communication systems. AM radio waves have λ 10 4 m while FM radio waves have λ few m. Easier to diffract long wave lengths than short ones AM waves can bend around buildings much more easily than FM waves.
21 Physics 201 p. 13/3 Spectrum Radio waves: λ 10 4 m 0.1m. Generated by electronic devices like an LC oscillator. Used in radio and television communication systems. AM radio waves have λ 10 4 m while FM radio waves have λ few m. Easier to diffract long wave lengths than short ones AM waves can bend around buildings much more easily than FM waves. Microwaves: λ 0.5m 10 4 m. Generated by electronic devices. Short wavelenghts. Suited for radars, atomic and molecular studies, etc... Microwave oven: λ = 0.122m.
22 Physics 201 p. 14/3 Spectrum Infrared waves: λ 10 3 m m. Generated by molecules and room-temperature objects. Readily absorbed by many materials. Applications: physical therapy, vibrational spectroscopy, etc.
23 Physics 201 p. 14/3 Spectrum Infrared waves: λ 10 3 m m. Generated by molecules and room-temperature objects. Readily absorbed by many materials. Applications: physical therapy, vibrational spectroscopy, etc. Visible light: λ = m (red) to λ m (violet). Maximum sensitivity of human eye at λ = m (yellow-green) Color of tennis balls.
24 Spectrum Ultraviolet waves: λ m m. Sun: big source of UV light sunburn. Sun screen: the higher the number the better the blocking of UV light becomes. Danger of cheap sun glasses: They do not block UV light and since the pupils are dilated there is more of UV light striking the lenses potential damage. Better not having those sun glasses because at bright sun light, the pupils are contracted less UV light striking the lenses. Most of UV light from the sun is absorbed by the ozone (O 3 ) layer. Very important layer in Physics 201 p. 15/3
25 Physics 201 p. 16/3 Spectrum X-rays: λ 10 8 m m. Generated by high-energy electrons bombarding metal targets. Used in medicine, and studies of crystal structure.
26 Physics 201 p. 16/3 Spectrum X-rays: λ 10 8 m m. Generated by high-energy electrons bombarding metal targets. Used in medicine, and studies of crystal structure. Gamma rays: λ m m. Emitted by radioactive nuclei such as 60 Co and 137 Cs. Also by high-energy cosmic rays entering the Earth s atmosphere.
27 Spectrum Physics 201 p. 17/3
28 Physics 201 p. 18/3 Energy in electromagnetic waves Energy density carried by the electric field: u E = 1 2 ɛ 0E 2.
29 Physics 201 p. 18/3 Energy in electromagnetic waves Energy density carried by the electric field: u E = 1 2 ɛ 0E 2. Energy density carried by the magnetic field: u B = 1 2µ 0 B 2.
30 Physics 201 p. 18/3 Energy in electromagnetic waves Energy density carried by the electric field: u E = 1 2 ɛ 0E 2. Energy density carried by the magnetic field: u B = 1 2µ 0 B 2. In an electromagnetic wave in vacuum or air: u E = u B. Total energy density: u = u E + u B = ɛ 0 E 2 = 1 µ 0 B 2
31 Physics 201 p. 19/3 Energy in electromagnetic waves Since c = 1 ɛ0 µ 0, u E = u B gives E = cb
32 Physics 201 p. 19/3 Energy in electromagnetic waves Since c = 1 ɛ0 µ 0, u E = u B gives E = cb Also: E rms = E max 2 B rms = B max 2
33 Energy in electromagnetic waves Physics 201 p. 20/3
34 Physics 201 p. 21/3 Energy in electromagnetic waves: Ex Sunlight enters the top of the Earth s atmosphere with an electric field whose rms value is 720 N/C. Find (a) the average total energy density of this electromagnetic wave and (b) the rms value of the sunlight s magnetic field. Solution: ū = ɛ 0 E 2 rms = ( C 2 /(N.m 2 ))(720 N/C) 2 = J/m 3.
35 Physics 201 p. 21/3 Energy in electromagnetic waves: Ex Sunlight enters the top of the Earth s atmosphere with an electric field whose rms value is 720 N/C. Find (a) the average total energy density of this electromagnetic wave and (b) the rms value of the sunlight s magnetic field. Solution: ū = ɛ 0 E 2 rms = ( C 2 /(N.m 2 ))(720 N/C) 2 = J/m 3. B rms = E rms c = T.
36 Physics 201 p. 22/3 Intensity of electromagnetic waves Intensity = Power/Area. After a time t, the waves travel a distance ct, passing through a surface of area A. Total energy = (Total energy density) x (Volume) = u(cta).
37 Physics 201 p. 22/3 Intensity of electromagnetic waves Intensity = Power/Area. After a time t, the waves travel a distance ct, passing through a surface of area A. Total energy = (Total energy density) x (Volume) = u(cta). Intensity: S = P A = U ta = u(cta) ta S = uc = cɛ 0 E 2 = c µ 0 B 2 = uc.
38 Physics 201 p. 23/3 Intensity of electromagnetic waves A nyodenium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric field has an rms value of N/C. Find the average power of each pulse that passes through a m 2 surface that is perpendicular to the laser beam. Solution: P = A S
39 Physics 201 p. 23/3 Intensity of electromagnetic waves A nyodenium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric field has an rms value of N/C. Find the average power of each pulse that passes through a m 2 surface that is perpendicular to the laser beam. Solution: P = A S S = cɛ 0 E 2 rms P = Acɛ 0 E 2 rms = W.
40 Doppler effects For a source moving with a speed very much smaller than the speed of light, the shift in frequency between source and observer is given by: f O = f S (1 ± v rel c ) f O : frequency observed by the observer. f S : frequency emitted by the source. v rel : speed of the source and observer relative to one another. +: source approaching the observer : source receding from the observer Applications: radar guns for example. Important application in astronomy: redshift Physics 201 p. 24/3
41 Physics 201 p. 25/3 Polarization Electromagnetic wave: Transverse wave oscillation of a field (e.g. the electric field) occurs along one direction linear polarization (taken by convention to be the direction of the electric field).
42 Physics 201 p. 25/3 Polarization Electromagnetic wave: Transverse wave oscillation of a field (e.g. the electric field) occurs along one direction linear polarization (taken by convention to be the direction of the electric field). Visible light: The electric field oscillates in a random direction light is unpolarized.
43 Physics 201 p. 25/3 Polarization Electromagnetic wave: Transverse wave oscillation of a field (e.g. the electric field) occurs along one direction linear polarization (taken by convention to be the direction of the electric field). Visible light: The electric field oscillates in a random direction light is unpolarized. How do we get polarized light from an unpolarized light?
44 Physics 201 p. 26/3 Polarization Polarizer: material such as a Polaroid that has a transmission axis Only the electric field which is parallel to that axis can pass through polarization.
45 Physics 201 p. 26/3 Polarization Polarizer: material such as a Polaroid that has a transmission axis Only the electric field which is parallel to that axis can pass through polarization. Analyzer: the second polarizer with an axis rotated by θ with respect to the first axis reduction in intensity.
46 Physics 201 p. 26/3 Polarization Polarizer: material such as a Polaroid that has a transmission axis Only the electric field which is parallel to that axis can pass through polarization. Analyzer: the second polarizer with an axis rotated by θ with respect to the first axis reduction in intensity. Malus law: S = S 0 cos 2 θ When θ = 90 0, no light passes through. Explain the IMAX 3D.
47 Polarization Physics 201 p. 27/3
48 Polarization Physics 201 p. 28/3
49 Polarization Physics 201 p. 29/3
50 Polarization Physics 201 p. 30/3
51 Polarization Physics 201 p. 31/3
52 Polarization Physics 201 p. 32/3
53 Polarization Physics 201 p. 33/3
54 Polarization Physics 201 p. 34/3
Announcements Self-inductance. Self-inductance. RL Circuit. RL Circuit, cont 3/11/2011. Chapter (not.9-.10) τ = R. Electromagnetic Waves
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