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Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 – p. 1/3 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. 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. 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 = 3.00 × 108 m/s. Physics 201 – p. 2/3 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. Physics 201 – p. 3/3 What are electromagnetic waves? Physics 201 – p. 4/3 What are electromagnetic waves? Physics 201 – p. 5/3 What are electromagnetic waves? Physics 201 – p. 6/3 What are electromagnetic waves? Physics 201 – p. 7/3 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? 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? Physics 201 – p. 8/3 Maxwell’s contribution Gauss’ law: EA = q/0 ⇒ q = 0 AE ⇒ ∆E I = ∆q = A 0 ∆t ∆t Physics 201 – p. 9/3 Maxwell’s contribution Gauss’ law: EA = q/0 ⇒ q = 0 AE ⇒ ∆E I = ∆q = A 0 ∆t ∆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 ΦE = EA. Physics 201 – p. 9/3 Maxwell’s contribution Maxwell: Imagine a fictitious current which he called a displacement current: ∆E E Id = 0 ∆Φ = A 0 ∆t = I. ∆t 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? Physics 201 – p. 10/3 Maxwell’s contribution The solution to Maxwell’s equations ⇒ Electromagnetic waves ⇒ Speed of the waves in vacuum: c = √10 µ0 = 3.00 × 108 m/s Physics 201 – p. 11/3 Maxwell’s contribution The solution to Maxwell’s equations ⇒ Electromagnetic waves ⇒ Speed of the waves in vacuum: c = √10 µ0 = 3.00 × 108 m/s Light is an electromagnetic wave! Physics 201 – p. 11/3 What is the electromagnetic spectru Accelerating charges ⇒ Radiation. 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 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. Physics 201 – p. 12/3 Spectrum Radio waves: λ ≈ 104 m − 0.1m. Generated by electronic devices like an LC oscillator. Used in radio and television communication systems. AM radio waves have λ ≈ 104 m while FM radio waves have λ ≈ f ew m. Easier to diffract long wave lengths than short ones ⇒ AM waves can bend around buildings much more easily than FM waves. Physics 201 – p. 13/3 Spectrum Radio waves: λ ≈ 104 m − 0.1m. Generated by electronic devices like an LC oscillator. Used in radio and television communication systems. AM radio waves have λ ≈ 104 m while FM radio waves have λ ≈ f ew 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. Physics 201 – p. 13/3 Spectrum Infrared waves: λ ≈ 10−3 m − 7 × 10−7 m. Generated by molecules and room-temperature objects. Readily absorbed by many materials. Applications: physical therapy, vibrational spectroscopy, etc. Physics 201 – p. 14/3 Spectrum Infrared waves: λ ≈ 10−3 m − 7 × 10−7 m. Generated by molecules and room-temperature objects. Readily absorbed by many materials. Applications: physical therapy, vibrational spectroscopy, etc. Visible light: λ = 7 × 10−7 m (red) to λ ≈ 4 × 10−7 m (violet). Maximum sensitivity of human eye at λ = 5.5 × 10−7 m (yellow-green) ⇒ Color of tennis balls. Physics 201 – p. 14/3 Spectrum Ultraviolet waves: λ ≈ 4 × 10−7 m − 6 × 10−10 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 (O3 ) layer. Very important layer in Physics 201 – p. 15/3 Spectrum X-rays: λ ≈ 10−8 m − 10−12 m. Generated by high-energy electrons bombarding metal targets. Used in medicine, and studies of crystal structure. Physics 201 – p. 16/3 Spectrum X-rays: λ ≈ 10−8 m − 10−12 m. Generated by high-energy electrons bombarding metal targets. Used in medicine, and studies of crystal structure. Gamma rays: λ ≈ 10−10 m − 10−14 m. Emitted by radioactive nuclei such as 60 Co and 137 Cs. Also by high-energy cosmic rays entering the Earth’s atmosphere. Physics 201 – p. 16/3 Spectrum Physics 201 – p. 17/3 Energy in electromagnetic waves Energy density carried by the electric field: uE = 12 0 E 2 . Physics 201 – p. 18/3 Energy in electromagnetic waves Energy density carried by the electric field: uE = 12 0 E 2 . Energy density carried by the magnetic field: uB = 2µ1 0 B 2 . Physics 201 – p. 18/3 Energy in electromagnetic waves Energy density carried by the electric field: uE = 12 0 E 2 . Energy density carried by the magnetic field: uB = 2µ1 0 B 2 . In an electromagnetic wave in vacuum or air: uE = u B . ⇒ Total energy density: u = uE + uB = 0 E 2 = µ10 B 2 Physics 201 – p. 18/3 Energy in electromagnetic waves Since c = E = cB √1 , 0 µ0 uE = uB gives Physics 201 – p. 19/3 Energy in electromagnetic waves Since c = E = cB Also: Erms = Brms = √1 , 0 µ0 uE = uB gives E√ max 2 B√ max 2 Physics 201 – p. 19/3 Energy in electromagnetic waves Physics 201 – p. 20/3 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: 2 ū = 0 Erms = (8.85 × 10−12 C 2 /(N.m2 ))(720 N/C)2 = 4.6 × 10−6 J/m3 . 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: 2 ū = 0 Erms = (8.85 × 10−12 C 2 /(N.m2 ))(720 N/C)2 = 4.6 × 10−6 J/m3 . Brms = Erms c = 2.4 × 10−6 T . Physics 201 – p. 21/3 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). 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 = S = uc = c0 E u(ctA) U = tA = tA = µc0 B 2 P A 2 = uc. Physics 201 – p. 22/3 Intensity of electromagnetic waves A nyodenium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric field has an rms value of 2.0 × 109 N/C. Find the average power of each pulse that passes through a 1.6 × 10−5 − m2 surface that is perpendicular to the laser beam. Solution: P̄ = AS̄ 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 2.0 × 109 N/C. Find the average power of each pulse that passes through a 1.6 × 10−5 − m2 surface that is perpendicular to the laser beam. Solution: P̄ = AS̄ 2 2 S̄ = c0 Erms ⇒ P̄ = Ac0 Erms = 1.7 × 1011 W . Physics 201 – p. 23/3 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: fO = fS (1 ± vrel c ) fO : frequency observed by the observer. fS : frequency emitted by the source. vrel : 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 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). 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. 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? Physics 201 – p. 25/3 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. 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. 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: S̄ = S̄0 cos2 θ When θ = 900 , no light passes through. Explain the IMAX 3D. Physics 201 – p. 26/3 Polarization Physics 201 – p. 27/3 Polarization Physics 201 – p. 28/3 Polarization Physics 201 – p. 29/3 Polarization Physics 201 – p. 30/3 Polarization Physics 201 – p. 31/3 Polarization Physics 201 – p. 32/3 Polarization Physics 201 – p. 33/3 Polarization Physics 201 – p. 34/3