(Pre- and) Post Tests and Surveys

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1 (Pre- and) Post Tests and Surveys All engineering students are being tested in their core courses this academic year at the beginning of the semester and again at the end of the semester. These data will be used to improve your learning experiences. Your responses to these tests & surveys will have no bearing on your course grade. I will not see your scores. I will only track whether or not you took the tests and surveys. There are four components to the pre and post test requirements: Two in-class exams; Two on-line surveys An exam and a survey both at the beginning and at the end of the semester. If you participate in all 4 components, you will get 100% on 2% of your grade If you miss any of the 4 components, you will get a zero for 2% of your grade. Second in-class exam Thursday, April 26 in lecture. Take survey TODAY and save confirmation page. Deadline Monday April 30 11:59 pm. Take the exams and surveys seriously Answer all parts to best of your abilities. If you do not take the exams and surveys seriously, you will get a zero. If you take the exams or surveys for someone else OR you ask someone to take the exams for you, you will not only get a zero but may be separated from the university because you have violated academic integrity. 1

2 Summer study opportunity: Plasma physics Undergraduate Plasma Physics Workshop July 18 through 20, 2018 at Princeton Plasma Physics Lab This workshop targets first and second-year undergrads and introduces them to plasma physics from an experimental and a theoretical perspective. The objective is for participants to gain an introductory understanding of the field of plasma physics and opportunities within. All travel, boarding and meals will be covered by PPPL. Underrepresented students are especially encouraged to apply. programs/workshop-plasma-physics-undergraduates 2

3 Announcements This week: course eval Required post test Thursday April 26 in lecture If miss lecture, limited opportunity for makeup; else zero for 2% of grade Homework 10 due Thursday April 26: Chapter Recitation on Friday April 27: Chapter 32. Quiz on Friday April 27: Homework 10, Lectures Final exam: Wednesday, May 9, :00 to 7:00 PM in Physics Lecture Hall. 30 multiple choice questions, 15 from Chapters 30-32, 15 cumulative Chapters Review session Tuesday, May 8 4 to 6 PM 227 Serin Physics & Astro All exams are closed-book, no calculators or other electronic devices allowed.

4 Final exam Announcements Wednesday, May 9, 2018 in lecture: 4:00 7:00 pm 30 multiple choice questions. 15 from Chapters 30-32, 15 from Chapters Exam review Tuesday, May 8, 4:00 6:00 pm 227 Serin Physics & Astro All exams are closed-book, no calculators or other electronic devices allowed. All questions will be multiple choice. For the final exam, you may bring with you three (3) "formula sheets", on 8.5 x 11 inch sheets of paper (OK to use both sides) on which you may hand write any formulae or diagrams or notes or problem solutions that might be helpful to you during the exam. Information on the sheets must be handwritten, no attachments are allowed. The numerical values of relevant constants will be provided to you. You should bring #2 pencils to the exams for the computer forms. Types of questions: Like I-clickers, simple numbers, formulae Study: Homework, I clickers, examples in textbook, collaborative+pre-rec Old exams: Free tutoring via MSLC:

5 Lecture 24 Tuesday April 24, 2018 Chap 32 continued: Electromagnetic Waves Energy, momentum Radiation pressure Standing waves 5

6 Model of E-M 6

7 Summary Chapter 32 E-M waves Maxwell s equations => electromagnetic waves Traveling at speed of light in vacuum Transverse; direction of propagation Sinusoidal E B E(x,t) = y E max cos(kx ωt) B(x,t) = z B max cos(kx ωt) E max = cb max c = 1 ε0 µ 0 = m/s 7

8 Mechanical Waves - review Wave motion is function of position (x) and time (t) y(x,t) = A cos(kx ωt) k = 2π λ ω = vk Where v=phase velocity of the wave E-M Waves propagating in +x direction E(x,t) = y E max cos(kx ωt) B(x,t) = z B max cos(kx ωt) Z Sinusoidal Waves y X E max = cb max 8

9 I clicker question The electric part of an electromagnetic wave moving in the +z direction is given by Which of the following statements about the y component of the magnetic field part is CORRECT? (A) B y cos(ky ωt) (B) B y cos(kz ωt) (C) B y sin(kz ωt) (D) B y = 0 E x = Asin(kz ωt), E y = E z = 0 (E) B y isgiven bysomeother expression. 9

10 I clicker answer The electric part of an electromagnetic wave moving in the +z direction is given by Which of the following statements about the y component of the magnetic field part is CORRECT? (A) B y cos(ky ωt) (B) B y cos(kz ωt) (C) B y sin(kz ωt) (D) B y = 0 E x = Asin(kz ωt), E y = E z = 0 (E) B y isgiven bysomeother expression. 10

11 Summary Chapter 32 E-M waves Maxwell s equations => electromagnetic waves Traveling at speed of light in vacuum Transverse; direction of propagation Sinusoidal E B Next: Energy and momentum of E-M waves c = 1 ε0 µ 0 = m/s E(x,t) = y E max cos(kx ωt) B(x,t) = z B max cos(kx ωt) E max = cb max 11

12 EM Energy (flow) in EM wave EM waves carry energy, in the electric and magnetic fields Recall energy densities B = E c = c = 1 ε0 µ 0 ε 0µ 0 E u = 1 2 ε 0 E u = u E + u B = 1 2 ε 0E µ 0 B 2 ( ) 2 = ε 0 E 2 = u 2µ 0 ε 0 µ 0 E Energy density of B-field = Energy density of E-field But E(position,time) => u(position,time) 12

13 EM Energy (flow) in EM wave Energy in volume dv=area x distance traveled in time dt Energy flow per unit time per unit area (in vacuum) = S S = 1 A c = 1 ε0 µ 0 du = udv = ε 0 E 2 (Acdt) du dt = ε 0cE 2 = ε ce(cb) = EB 0 µ 0 S points in direction of energy flow = direction of propagation of the EM wave Ø The Poynting vector Units: power/unit area S = 1 µ 0 E B Because E,B(position,time) => S(position,time) 13

14 c = 1 ε0 µ 0 EM Energy flow/intensity in EM wave Assume sinusoidal wave traveling in +x direction E(x,t) = y E max cos(kx ωt) S(x,t) = 1 µ 0 Direction = +x direction Magnitude Time average of S: B(x,t) = z B max cos(kx ωt) y E max cos(kx ωt) z B max cos(kx ωt) S = 1 µ 0 E max B max cos 2 (kx ωt) = 1 µ 0 E max B max S = 1 µ 0 E B 1+ cos2(kx ωt) [ ] Time average of cos=0 I = S av = E maxb max = E 2 max µ Intensity I=S 0 2µ 0 c = 1 2 ε ce 2 0 max av 14

15 I = S av = E max B max µ 0 = E 2 max 2µ 0 c = 1 2 ε 0 ce 2 max I clicker question Imagine that when you switch on your lamp, you increase the intensity of light shining on your textbook by a factor of 16. By what factor does the average electric field strength in this light increase? A. Factor of 256 B. Factor of 16 C. Factor of 4 D. Factor of 2 E. Factor of 1 15

16 I = S av = E max B max µ 0 = E 2 max 2µ 0 c = 1 2 ε 0 ce 2 max I clicker answer Imagine that when you switch on your lamp, you increase the intensity of light shining on your textbook by a factor of 16. By what factor does the average electric field strength in this light increase? A. Factor of 256 B. Factor of 16 C. Factor of 4 D. Factor of 2 E. Factor of 1 16

17 I = S av = E 2 max 2µ 0 c Power of the source Imagine that when you switch on your lamp, you increase the intensity of light shining on your textbook by a factor of 16. If your book is r=1 m from your lamp, how intense is the light source? (i.e., what is the total energy flow/unit time out of the lamp?) P = " S d A = I(4πr 2 ) av I = P 4πr 2 17

18 Comet dust tails Rad pressure example 18

19 Momentum flow & pressure in EM wave Electromagnetic waves carry momentum EM radiation is made up of particles = photons p = energy c that carry energy and momentum Momentum density: dp dv = 1 c dp dv = S c 2 d(energy) dv = ε 0 E 2 Average rate of momentum transfer/area: where dv=acdt c = ε 0 EcB c = ε 0 EB µ 0 µ 0 = S c 2 dp dt E = cb c = 1 ε0 µ 0 S = 1 µ 0 1 A = S av c = I c E B 19

20 Momentum flow & pressure in EM wave Electromagnetic waves carry momentum Average rate of momentum transfer/area: dp dt 1 A = S av c = I c Pressure = force/unit area=(dp/dt)/unit area Amount of pressure depends upon whether EM wave is Totally absorbed p rad = S av c = I c Totally reflected (change in momentum doubled) p rad = 2S av c = 2I c 20

21 Consider linearly polarized EM wave traveling in -x direction on a perfect conductor E must be zero everywhere on the y-z conducting plane But incident E 0 in y-z plane Net E field =0 = incident + reflected oscillating E-field E y (x,t) = E max B z (x,t) = B max cos(kx +ωt) cos(kx ωt) Standing EM waves [ ] [ cos(kx +ωt) cos(kx ωt) ] cos(a ± B) = cos AcosB sin Asin B E y (x,t) = 2E max sin kxsinωt B z (x,t) = 2B max coskx cosωt 21

22 Standing waves E y (x,t) = 2E max sin kxsinωt B z (x,t) = 2B max coskx cosωt Standing EM waves in a cavity E has to be zero at x=0 and x=l Defines normal modes L λ n = 2L n n = 1,2,3... f n = c λ n = n c 2L 22

23 Standing waves E y (x,t) = 2E max sin kxsinωt B z (x,t) = 2B max coskx cosωt At x=0, E always zero E=0 where sinkx=0 x = 0, λ 2, λ, 3λ 2... Ø Nodal planes of E kx = 0, π, 2π... Standing EM waves Antinodal planes of E (when E=max) = Nodal planes of B when coskx=0 Note E(t) is sinωt and B(t) is cosωt x = λ 4, 3λ 4, 5λ 4... kx = π 2, 3π 2, 5π 2... Ø E and B fields are out of phase when in a standing wave 23

24 Standing waves E y (x,t) = 2E max sin kxsinωt B z (x,t) = 2B max coskx cosωt At x=0, E always zero E=0 where sinkx=0 x = 0, λ 2, λ, 3λ 2... Nodal planes of E kx = 0, π, 2π... Standing EM waves Node Anti-node L = 3λ 2 Antinodal planes of E (when E=max) = Nodal planes of B when coskx=0 Note E(t) is sinωt and B(t) is cosωt x = λ 4, 3λ 4, 5λ 4... kx = π 2, 3π 2, 5π 2... Ø E and B fields are out of phase when in a standing wave 24

25 Standing wave nodal planes for E and B fields Given standing EM wave with frequency f=30 MHz Wavelength λ = v f = m/s /s = 10 m What is distance between nodal planes of E-field? Nodal planes of E field when x = 0, λ 2, λ, 3λ 2... Distance between nodal planes = λ/2 = 5 m4=2.5 m

26 Standing wave nodal planes for E and B fields Given standing EM wave with frequency f=30 MHz Wavelength λ = v f = m/s /s = 10m Nodal planes of E field when x = 0, λ 2, λ, 3λ 2... Distance between nodal planes = λ/2 = 5 m What is distance between nodal plane of E-field and nodal plane of B- field? Nodal planes of B field when (also anti-nodal planes of E field) x = λ 4, 3λ 4, 5λ 4... Distance between nodal planes of E and B fields = λ/4=2.5 m

27 1 sin acosa = sin 2a 2 S av =< 1 µ 0 E B > The drawing shows a sinusoidal electromagnetic standing wave. Which of the following statements about the average (averaged over either x or t) Poynting vector in this wave is CORRECT? I clicker question A. The average Poynting vector in this wave points along the x-axis. B. The average Poynting vector in this wave points along the y-axis. C. The average Poynting vector in this wave points along the z-axis. D. The average Poynting vector in this wave is zero. E. None of the above statements about the average Poynting vector in this wave is correct. 27

28 1 sin acosa = sin 2a 2 S av =< 1 µ 0 E B > The drawing shows a sinusoidal electromagnetic standing wave. Which of the following statements about the average (averaged over either x or t) Poynting vector in this wave is CORRECT? I clicker answer A. The average Poynting vector in this wave points along the x-axis. B. The average Poynting vector in this wave points along the y-axis. C. The average Poynting vector in this wave points along the z-axis. D. The average Poynting vector in this wave is zero. E. None of the above statements about the average Poynting vector in this wave is correct. 28

29 sin acosa = 1 sin 2a 2 S av =< 1 µ 0 E B > I clicker solution The drawing shows a sinusoidal electromagnetic standing wave. Which of the following statements about the average (averaged over either x or t) Poynting vector in this wave is CORRECT? S av =< 1 µ 0 E B >=< 1 µ 0 E max sin kxsinωtb max coskx cosωt > =< 1 µ 0 E max B max sin kx coskxsinωt cosωt > =< 1 µ 0 E max B max { 1 2 sin 2kx 1 2 sin 2ωt} >= 0 29

30 Maxwell s equations in vacuum, free space Ø EM waves E = cb c = 1 = m/s ε0 µ 0 Direction of propagation E B Sinusoidal Power/unit area = Poynting vector Summary Chapter 32 E(x,t) = y E max cos(kx ωt) B(x,t) = z B max cos(kx ωt) S = 1 µ 0 E B Ø Intensity of EM wave Radiation pressure of EM wave Standing EM waves I = S av = E max B max µ 0 = 1 2 ε 0cE 2 max p rad (absorbed) = S av c = I c p rad (reflected) = 2S av c = 2I c 30

31 Standing E-M waves E and B 90 out of phase E y (x,t) = 2E max sin kxsinωt B z (x,t) = 2B max coskx cosωt Nodes where E=0; antinodes B=max: Antinodes where E=max; nodes B=0: Standing waves in a cavity Summary Chapter 32 (cont) kx = 0, π, 2π... kx = π 2, 3π 2, 5π chapters_2017_jan_1/quantum_theory_origins/index.html 31

32 See you on Thursday Summary of the semester Required post test Thursday April 26 Final Exam Wednesday, May 9 32

Clicker Question. Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no

Clicker Question. Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following