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Transcript
Electromagnetic Waves • Electromagnetic waves are traveling waves of electric and magnetic fields. • Electromagnetic waves come in a wide range of wavelengths. There is more to the spectrum than the rainbow. • Long wavelengths act like waves, short wavelengths like particles. Or, more precisely, like photons. 1 Warming Up. A metal wire is resting on a U-shaped conducting rail. The rail is fixed in position, but the wire is free to move. If the magnetic field is increasing in strength, what is the direction of the induced current? a.Clockwise b.Counterclockwise What is the direction of the force on the wire? a.To the left b.To the right 2 Now, think... A metal wire is resting on a U-shaped conducting rail. The rail is fixed in position, but the wire is free to move. If the magnetic field is increasing in strength, this induces a current in the wire. How do the charges know to move? 3 A changing magnetic field induces an electric field. A changing electric field induces a magnetic field too. One of the 10 coolest things ever discovered 4 The Inductor L is the inductance; the unit is the Henry. (H) 5 LC Circuits 6 Tuned Circuits 7 Unifying Electricity and Magnetism ! ρ ∇⋅E = ε0 ! ∇⋅B = 0 ! ! ∂B ∇×E =− ∂t ! ! ! ∂E ∇ × B = µ0 j + µ0ε 0 ∂t 8 The electromagnetic pulse. An accelerated charge emits a pulse of electric and magnetic fields. This pulse travels through space. Maxwell’s equations say the speed should be: v= 1 = 3.00 × 10 8 m/s ε 0 µ0 9 netism wondered about this and hypothesized th an induced magnetic field. This hypothesis leads to a surprising conclus induce an electric field in the absence of any ch can induce a magnetic field in the absence of any establish self-sustaining electric and magnetic f u currents. A changing electric field E creates a ma just the right way to recreate the electric field, wh to again recreate the magnetic field, with the f electromagnetic induction. In fact, electric and m free from any charges or currents, if they take the The electromagnetic wave. An oscillating charge will emit an electromagnetic wave. It’s a wave of electric and magnetic fields. electromagnetic wave. 1. The wave is a sinusoidal traveling wave, Electromagnetic Waves with frequency f and wavelength l. u E0 10 In order to sustain itself and travel through sp have a very specific geometry, shown inu FIGUR magnetic wave is a transverse wave. E and B well as perpendicular to the direction of travel. A mathematical analysis shows that such a w FIGURE 25.25 A sinusoidal y Properties of Electromagnetic Wa Wavelength l E vem = u E u vem B0 u B z u u E u B x u 2. E and B are perpendicular to each other and to the direction of u u 3. E and B are in phase; travel. Thus an thatare is, they have electromagnetic Electromagnetic Waves Waves. matching crests, wave is a troughs, transverse wave. c = f λ and zeros. c 3.0 × 10 8 m/s f = = λ λ 1 f ∝ λ • • Increasing wavelength Decreasing frequency Increasing frequency Decreasing wavelength 1 2P0m where P0 and m0 are the permittivity and permea for electric and magnetic fields. If you insert t stants, you find vem = 3.00 * 108 m/s. This is a speed of light! In a vacuum, all electromagnetic waves must we11call the speed of light and for which we use the first to make this analysis, made a bold leap tromagnetic wave. We studied the wave proper we didn’t discuss just what is “waving.” Now w and magnetic fields. The amplitudes of the electric and magnetic on the wave, the electric and magnetic field stre E =c B Figure 25.25 shows the values of the electric a single line, the x-axis. u An E vector pointing in the y-dire x-axis, where the vector’s tail is, the electric f 12 a certain strength. Nothing is “reaching” to a NOTE ▶ FM vs. AM An FM station transmits at 100 MHz, corresponding to a wavelength of 3.0 m. An AM station transmits at 1000 kHz, which is 1.0 MHz. What is the corresponding wavelength? Think about ratios. The frequency decreases by a factor of 100. What happens to the wavelength? c = fλ 13 FM & AM Radio FM: Pick up electric field AM: Pick up magnetic field 1 λ 4 14 Helpful Relationships E = hf = hc λ h = 4.14 × 10 −15 eVis E (in eV) = 1240 λ (in nm) 15 Atomic Energies 16 Red vs. Blue, Part I. A red pen laser emits light of wavelength 670 nm. A blue pen laser emits light of wavelength 470 nm. Which has a higher photon energy, the red or the blue? E = hf 17 Red vs. Blue, Part II. A red pen laser emits light of wavelength 670 nm. A blue pen laser emits light of wavelength 470 nm. Both lasers emit the same power, the same number of joules per second. Which laser emits more photons per second? E = hf 18 The Electromagnetic Spectrum Particle-y Depends Wave-ish 19 The Electromagnetic Spectrum Wave Wavelength Frequency FM Radio 100 MHz Microwave 1.9 GHz Far IR 10 µm Visible 500 nm Ultraviolet 290 nm Photon energy 20 The Electromagnetic Spectrum 21 Basic Relationships The speed of electromagnetic waves A. depends on the wavelength B. depends on the photon energy C. is the same as the speed of sound D. is the same for all waves regardless of wavelength 22 Basic Relationships A typical analog cell phone has a frequency of 850 MHz; a digital phone a frequency of 1950 MHz. Compared to the signal from an analog cell phone, the digital signal has ! A. ! longer wavelength and lower photon energy ! B. ! longer wavelength and higher photon energy ! C. ! shorter wavelength and lower photon energy ! D. ! shorter wavelength and higher photon energy 23 Basic Relationships A radio tower emits two 50 W signals, one an AM signal at a frequency of 850 kHz, one an FM signal at a frequency of 85 MHz. Which signal has more photons per second? Explain. ! A. ! The AM signal has more photons per second. ! B. ! The FM signal has more photons per second. ! C. ! Both signals have the same photons per second. 24 Intensity Intensity is a ratio of power to area: From Chapter 15 P I= A My laser pointer has a total output power of about 1.0 mW. When I shine it on the screen, it spreads out to make a spot about 1.0 mm in diameter. What is the intensity of the light in this spot? How does this compare to the intensity of sunlight on the ground at high noon on a summer day (which is approximately 1100 W/m2)? 25 Energy and Field Strength E0 = 2I cε 0 B0 = E0 c E0 = cB0 26 The Microwave Oven E0 = 2I cε 0 B0 = E0 c E0 = cB0 Inside the cavity of a microwave oven, the 2.4 GHz electromagnetic waves have an intensity of 5.0 kW/m2. a. What is the strength of the electric field? b. The magnetic field? 27 Intensity Variation for Spherical Wave I= Psource 4π r 2 28 A digital cell phone emits a 1.9 GHz electromagnetic wave with total power 0.60 W. • At a cell phone tower 2.0 km away, what is the intensity of the wave? (Assume that the wave spreads out uniformly in all directions.) • What are the electric and magnetic field strengths at this distance? I= Psource 4π r 2 E0 = 2I cε 0 B0 = E0 c 29 Polarization 30 Navigating By The Sky Polarization of skylight Bee eyes detect polarization 31 Biological Effects of EM Radiation Long wavelength Wave-ish Short wavelength Particle-y 32 Talking On the Phone... How Dangerous? P = 0.60 W f = 1.9 GHz Compute: 1) Intensity 2) Field strength 3) Photon energy at 5.0 cm 33 What are the photon energies corresponding to the following wavelengths? a. b. c. d. Near IR, 1000 nm Far red end of the spectrum, 750 nm Far blue end of the spectrum, 400 nm Near UV, 290 nm E (in eV) = 1240 λ (in nm) 34 Atomic Radiation Visible spectrum: Approx. 400 - 750 nm 35 100 Watts = 4 Watts? A typical incandescent lamp has a filament at a temperature of approximately 2500 °C. What is the peak wavelength of the emission? 36 Single-Photon Detection Molecules are tuned to particular photon energies. 37 Visible Light, Near IR and UV 3 different cones tuned to different photon energies 38 The band gap of the silicon used to make the CCD detector in a black and white security camera is 1.12 eV. Photons with energy greater than this will be detected. • What wavelength does this correspond to? • In what part of the spectrum is this? 39 Radiation N.B. e=0.97 for skin of any color. Seal thermal window Pit viper 40 You Look Positively Radiant A typical human has a surface area of about 1.8 m2. All skin, regardless of color, has an emissivity of about e=0.97. How much power does a person’s body radiate at normal skin temperature? (About 33 °C, or 306 K) What is the peak wavelength of the emission? Pit Vipers 41 1600 cells Raw Processed 42 Short wavelength = high photon energy Germicidal lamps 254 nm 4.9 eV Tanning beds 365 nm 3.4 eV 43 Creating X rays If an electron is accelerated through a 5.0 kV potential difference, what is the maximum photon energy of the resulting x ray? What is the wavelength? 44 Using X rays 45