Download CHAPTER 32 ELECTROMAGNETIC WAVES

CHAPTER 32 ELECTROMAGNETIC WAVES BASIC CONCEPTS PROPAGATION OF LIGHT ELECTROMAGNETIC SPECTRUM ENERGY IN ELECTROMAGNETIC WAVES ‐ THE POYNTING VECTOR 1 MAXWELL’S EQUATIONS Describe electromagnetic waves. 2 Maxwell used these equations to predict the propagation of electromagnetic waves, light. Assume an E‐M wave moving in the direction. 3 First apply Gauss’s law Flux is zero. This would not be true if either had components in the direction. 4 Now apply Faraday’s Law. 5 Now for Apply to in figure. 6 Because ·
0; ·
0; ·
0 Then Gives And thus 7 Next apply Ampere’s Law No capacitors thus Thus 8 9 Integrate around 10 Because ·
0; ·
0; ·
0 Thus Gives And 11 We have from Faraday’s Law We have from Ampere’s Law Thus we get (putting the second in the first) And 12 The E‐M Wave will travel in the direction at a speed of (where ). and no components in the direction. 13 ELECTROMAGNETIC WAVES 1. The solutions of Maxwell’s third and fourth equations are wavelike where both E and B satisfy the same wave equation. 2. Electromagnetic waves travel through . empty space with speed of light, 3. The electric and magnetic field components of plane electromagnetic waves are perpendicular to each other and perpendicular to the direction of propagation. 4. The relative magnitudes of E and B in empty space are related by . 5. Electromagnetic waves obey the principle of superposition.
14 The equations for can be written. They are And Defining the wave The wavelength is the distance along the wave from a point to the next point where the waves starts to repeat. The frequency is the number of times per second a point on the wave passes through a cycle. 15 The spectrum What are electromagnetic waves? 16 Energy in E‐M Waves Remember from Chapter 24 Energy of Electric Field And From Chapter 30 Energy of Magnetic Field Thus for a region with both fields 17 Using we can simplify Energy density for E‐M Wave 18 Consider region of space where E‐M wave propagating in . Energy in region defined by by will be energy that passed through area 19 Energy in region is energy density multiplied by volume. The energy per unit time through will be And the energy per unit time per unit area will be 20 We will call this . Using We get 21 The energy per unit area per unit time passing through an area with an E‐M wave. We define a vector, the Poynting vector, to be 22 The direction of the Poynting vector is the direction of propagation of the wave. The magnitude of the Poynting vector is the energy per unit time per unit area (power per unit area) delivered by the wave. Calculate the average power delivered (Books way). 23 So the magnitude of will be 1
cos 2
2
Use 2
1
2 (Page A‐3 in Book) 24 1
2
2 Average cycle 2
0 Therefore average 2
My method 25 Plot this 2
2
Use 26 2
2
2
The book’s value. Measuring the Speed of Light 27 TWO NEW SCIENCES By GALILEO Simplicio: Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired, at a great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval. Sagredo: Well, Simplicio, the only thing I am able to infer from this familiar bit of experience is that sound, in reaching our ear, travels more slowly than light; it does not inform me whether the coming of the light is instantaneous or whether, although extremely rapid, it still occupies time. 28 Distance Earth‐Jupiter 6x1011m
Observe image 38 min late. 6 10
38 60 ⁄
2.76 10
/
29 30 31