Physics 212 Lecture 23 Slide 1 Main Point

Physics 212 Lecture 23, Slide 1

Main Point 1 First, we established that the electric and magnetic field oscillations in a plane electromagnetic wave are in phase with each other and that the direction of propagation of these waves can be obtained from the cross product of E and B. We determined that the frequency (and wavelength) of electromagnetic waves vary by almost 20 orders of magnitude from radio waves to photons at the Tevatron at Physics 212 Lecture 23, Slide 2 Fermilab.

Main Point 2 Second, we introduced the Doppler shift, the frequency shift due to the relative motion of the source of these waves and the observer. Physics 212 Lecture 23, Slide 3

Main Point 3 Finally, we determined that the energy density in the electric and magnetic fields in an electromagnetic wave are equal. We defined the intensity of the wave as the averate power transmitted per unit area. We formalized the energy transport by introducing the Poynting vector, defined as the cross product of the electric and magnetic fields, normalized by m 0. The direction of this vector is the direction of propagation of the wave while its magnitude is equal to the instantaneous power in Physics 212 Lecture 23, Slide 4 the wave per unit area.

Plane Waves Physics 212 Lecture 23, Slide 5

Checkpoint 1 a Physics 212 Lecture 23, Slide 6

Physics 212 Lecture 23, Slide 7

Checkpoint 1 b Which of the following actions will increase the energy carried by an electromagnetic wave? A. Increase E keeping w constant C. Both of the above will increase the energy B. Increase w keeping E constant D. Neither of the above will increase the energy Physics 212 Lecture 23, Slide 8

Physics 212 Lecture 23, Slide 9

Checkpoint 2 a c=3. 0 x 108 m/s Physics 212 Lecture 23, Slide 10

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Checkpoint 2 b A) B) C) ficlicker = 900 MHz Physics 212 Lecture 23, Slide 12

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Doppler Shift +v if they are approaching -v if they are separating f f’ v or f f’ v Physics 212 Lecture 23, Slide 14

Police radars get twice the effect since the EM waves make a round trip: If f = 24, 000, 000 Hz (k-band radar gun) c = 300, 000 m/s v b f’ f’-f 30 m/s 1. 000 x 10 -7 24, 000, 004, 800 4800 Hz 31 m/s 1. 033 x 10 -7 24, 000, 004, 959 4959 Hz Physics 212 Lecture 23, Slide 15

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Waves Carry Energy Physics 212 Lecture 23, Slide 17

Intensity = energy delivered per unit time, per unit area (U = energy) Length = c dt Area = A Sunlight on Earth: I ~ 1000 J/s/m 2 ~ 1 k. W/m 2 Physics 212 Lecture 23, Slide 18

Physics 212 Lecture 23, Slide 19

Light has Momentum! If it has energy and its moving, then it also has momentum: Analogy from mechanics: For E-M waves: pressure Radiation pressure Physics 212 Lecture 23, Slide 20

PHOTONS We believe the energy in an e-m wave is carried by photons Question: What are Photons? Answer: Photons are Photons possess both wave and particle properties Particle: Energy and Momentum localized Wave: They have definite frequency & wavelength (fl = c) Connections seen in equations: E = hf p = h/l Planck’s constant h = 6. 63 e-34 J-s Question: How can something be both a particle and a wave? Answer: It can’t (when we observe it) What we see depends on how we choose to measure it ! The mystery of quantum mechanics: More on this in PHYS 214 Physics 212 Lecture 23, Slide 21

Calculation 1 y x An electromagnetic wave is described by: where is the unit vector in the +y direction. z Which of the following graphs represents the z-dependence of B x at t = 0? (A) (B) (C) (D) Physics 212 Lecture 23, Slide 22

Calculation 2 An electromagnetic wave is described by: y x z What is the form of B for this wave? (A) (C) (B) (D) Physics 212 Lecture 23, Slide 23

Calculation 3 An electromagnetic wave is described by: Which of the following plots represents Bx(z) at time t = p/2 w ? (A) (B) (C) (D) Physics 212 Lecture 23, Slide 24

Calculation 4 A certain unnamed physics professor was arrested for running a stoplight. He said the light was green. A pedestian said it was red. The professor then said: “We are both being truthful; you just need to account for the Doppler effect !” Is it possible that the professor’s argument is correct? (lgreen = 500 nm, lred = 600 nm) (A) YES (B) NO Physics 212 Lecture 23, Slide 25

Physics 212 Lecture 23, Slide 26