chapter32---PHY 131 JAB - Chapter 32 Electromagnetic waves...

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1 Chapter 32: Electromagnetic waves §32.1: Maxwell’s equations and electromagnetic waves
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2 Maxwell’s equations (in vacuum) in integral and differential form. dt d I d dt d d d Q d e 0 0 enc 0 B 0 enc 0 Φ + = Φ - = = = ∫∫ ∫∫ ε μ μ ε l B l E A B A E t t + = × - = × = = E J B B E B E 0 0 0 0 0 ε μ μ ε ρ z y x ˆ ˆ ˆ z y x + + = where
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3 Maxwell’s equations in differential form can be manipulated into the form 2 2 2 2 1 t c = E E 2 2 2 2 1 t c = B B These are wave equations. The speed of these waves is c. ( )( ) m/s 10 00 . 3 Tm/A 10 4 /Nm C 10 85 . 8 1 1 8 7 2 2 12 0 0 × = × × = = - - π μ ε c
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4 In 1675 Ole Römer presented a calculation of the speed of light. He used the time between eclipses of Jupiter’s Gallilean Satellites to show that the speed of light was finite and that its value was 2.25 × 10 8 m/s. Fizeau’s experiment of 1849 measured the value to be about 3 × 10 8 m/s. (Done before Maxwell’s work.) §32.2: Plane electromagnetic waves and the speed of light
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5 The following properties can be deduced from the wave equations and their solutions: 1. Both E and B are perpendicular to the direction of motion of the wave. The waves are transverse. 2. E and B are mutually orthogonal 3. E × B gives the direction of wave propagation 4. The fields vary sinusoidally and are in phase
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6 A solution to the (1-d) wave equations is ( ) ( ) ( ) ( ) z B y E ˆ sin , ˆ sin , m m t kx B t x t kx E t x ω ω - = - = These describe electromagnetic waves traveling in the +x direction. These expressions have the mathematical form of a traveling wave. c B E = m m Note: §32.3: Sinusoidal electromagnetic waves
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7
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8 Definitions f π ω 2 = Is the wave number; λ is the wavelength of the wave λ π 2 = k Is the (angular) frequency Note: c = λ f and is true for all EM waves; EM waves do not need a medium to travel though
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9 Example: Have a traveling wave ( ) ( ) ( ) t x t x y 72 . 2 1 . 72 sin m 00327 . 0 , - = Have: A= 0.00327 m; ω = 2.72 rad/sec; k = 72.1 rad/m The frequency of the wave is Hz 433 . 0 2 = = π ω f The wavelength of the wave is m 0.0821 2 = = k π λ The wave’s speed is m/s 377 . 0 = = f v λ
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10 A stationary charge produces an electric field.
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