sem5 em cornell edu phys2208 lecture01 41

1. Physics 2208

2. Today: Electric charge Coulombs law

3. Our Promise We will teach you physics that matters to you. We will treat you with respect. We will help you.

4. Physics 2208 Spring 2012 Lecturer: Matthias Liepe Senior Staff: Glenn Case, Glenn Fletcher Course Web Site: www.blackboard.cornell.edu Lecture notes Homework assignments and solutions Please sign Sign-up Sheet if you can not access the page and need to be added to Blackboard

5. Texts: Fundamentals of Physics, 9th ed., Vol. 2, by Halliday, Resnick, and Walker P2208 Lab Manual 2012 I-Clicker: Please register your I-Clicker for this semester at http://fit.cit.cornell.edu/atcsupport/pollsrvc/ . Academic Integrity: We take issues of academic integrity extremely seriously.

6. Homework assignments: Handed out/due every Wednesday. HW 1 due next week Wednesday. Grading based on effort. Cooperative Learning Problems: Assigned in section. You'll work on them in teams. Labs One during most weeks. No lab book is required. Turn in the completed lab manual pages. Labs start next week, in Rock B54. You must attend all labs! You must attend the lab section you are signed up for! There will be no make-up labs! Quizzes: One each week, in recitation. Based on previous weeks lectures, recitation and lab work. Start week of Feb. 6. Participation: Lecture participation, recitation participation, lab part.

7. Exams: Prelim 1: Thursday, March 1 Prelim 2: Thursday, April 5 Final: Monday, May 14 Grading: Exams: 65% (20% P1, P2, 25% Final) Recitation, HW, Lab, part.: 35% Exams will not be curved (unless we goof). Section grades will be adjusted for differences between TAs. Help each other to learn, and no one will lose!

8. We will try our best to accommodate everyone who wants to take Physics 2208, but this class is very full. Please see Rosemary French (121 Clark Hall) for help signing up. Lectures on the same day are identical and you can attend either one, no matter which one you signed up for. You must attend the section and labs you are signed up for! See Rosemary French if you need to change sections /labs because of direct conflicts. Registration issues should be settled in the first two weeks.

9. Course Objective: To introduce you to the ideas and tools of physics relevant to careers in medicine, biology, and other science-related areas. Syllabus: Concepts will be illustrated with applications. Electric charge, field, and forces Electric potential Electric currents and circuits Magnetic fields and forces Sources of magnetic fields Electromagnetic waves Geometrical optics Interference and diffraction Relativity Quantum mechanics Nuclear and particle physics

10. Math Skills for Physics 2208 Unlike 1101, 2208 is officially calculus-based. However, you need only understand the basic notions of a derivative and an integral.

11. Getting Help in P2208 1. Study room/ Office Hours All office hours will be held in Clark Hall, second floor, next to room 282. The study room is open: Mondays: 1 6 PM Tuesdays: 1 9 PM Wednesdays: 1 6 PM Thursdays: 1 6 PM Fridays: 1 6 PM Saturdays: 1 6 PM Sundays: study room closed Phys2208 staff will be present during most of the time the study room is open (see detailed schedule on study room door)

12. Getting Help in P2208 2. Prof. Liepes Help me! Office Hours Wednesdays, 3- 4 PM in 302 PSB. See me if you feel overwhelmed by the material, need study tips, are concerned about your performance

13. Getting Help in P2208 3. The Learning Strategies Center - B14 Rock Focused on those students needing remedial help in math and physics LSC office hours: Mon-Thurs: 2:30-5:30 pm and 6:30-9:30 pm Friday: 2:30-5:30 pm Saturday: closed Sunday: noon - 9 pm

14. Getting Help in P2208 4. Counseling and Psychological Services (CAPS) - Gannett Health Center Where to go if you are feeling unusually anxious, stressed or depressed, and especially if these feelings are interfering with your ability to perform in the course. Don't dismiss this option: Psychological issues are one of the most important controllable factors affecting student performance in challenging courses.

15. Keys to Success in Physics 2208 1. You can't learn how to do physics by reading the text or the solutions manual! Do lots and lots of problems, both on your own and in groups. Your ability to solve problems on your own is the gold standard against which to assess your understanding.

16. Keys to Success in Physics 2208 2. You get most of the points in recitation, lab and HW for showing up and making a good effort. Don't throw these points away! Missed work carries a huge grade penalty: missing half the homework is roughly equivalent to the difference between getting an "A" and a "C" on a prelim! Do all the assigned work.

17. Keys to Success in Physics 2208 3. Maintain a consistent effort. Attend lectures, recitations and labs through- out the semester. Exam Performance Vs. Participation Score - P207 Fall 2003 0 0.2 0.4 0.6 0.8 1 1.2 Prelim 1 Prelim 2 Final Exam (ExamScore)/(Class Mean) 100% 90% 80% 70% 60% B. < C. = 2 0 21 4 r qq 2 0 21 4 r qq 2 0 21 4 r qq

30. q2 q1 The electrostatic force by the shell of uniform charge q2 an the particle of charge q1 is A. Pointing to the left B. Pointing to the right C. Pointing up D. Pointing down E. zero

31. Shell Theorem: A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shells charge were concentrated at its the shells center. If a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell.

32. Conductors and Insulators

33. A PVC rod is rubbed with wool to charge the rod negative and then broad near a floating metal coated He-balloon, which has no net charge. The electrostatic force between the rod and the balloon will A. Push the balloon away B. Attract the balloon C. Nothing will happen.

34. A Plexiglas rod is rubbed with vinyl to charge the rod positive and then broad near a floating metal coated He-balloon, which has no net charge. The electrostatic force between the rod and the balloon will A. Push the balloon away B. Attract the balloon C. Nothing will happen.

35. Copy Machine 1.) Charging: cylindrical drum is electrostatically charged by a high voltage wire. 2) Exposure: A bright lamp illuminates the original document, and the white areas of the original document reflect the light onto the surface of the photoconductive drum. The areas of the drum that are exposed to light become conductive and therefore discharge to ground. 3) Developing: The toner is positively charged. When it is applied to the drum to develop the image, it is attracted and sticks to the areas that are negatively charged (black areas). 4) Transfer: The resulting toner image on the surface of the drum is transferred from the drum onto a piece of paper with a higher negative charge than the drum. 5) Fusing: The toner is melted and bonded to the paper by heat and pressure rollers.

36. Recap Lecture 3

37. Today: E-paper Electric Fields Electrolocation

38. A plastic balloon is charged negatively and then hold to a non-conducting wall. When released, the balloon will A. Drop B. Stick to the wall C. Cant be sure

39. Electronic Paper Paper consists of a sheet of very small transparent capsules, each about 40 micrometers across. Each capsule contains an oily solution containing black dye (the electronic ink), with numerous white titanium dioxide particles suspended within. The white particles are slightly negatively charged. Applying a negative charge to the surface electrode repels the particles to the bottom of local capsules, forcing the black dye to the surface and giving the pixel a black appearance. Reversing the voltage has the opposite effect - the particles are forced to the surface, giving the pixel a white appearance.

40. Electric Fields

41. A very small stationary negative test charge qt (qt 0) at a certain location experiences a net electric force in the x direction. What is the direction of the electric field (not due to qt) at qts location? A. x B. x C. Cant tell for sure.

42. What is the electric field direction at this location if qt is removed? A. x B. x C. Cant tell for sure.

43. What is the direction of the electric field at point A? Q Q D D y x A B C A. B. C. D. E. None of the above

44. What is the direction of the electric field at point B? Q Q D D y x A B C A. B. C. D. E. None of the above

45. Electrolocation: In active electrolocation, the animal senses its surrounding environment by generating electric fields and detecting distortions in these fields using electroreceptor organs. This is important in ecological niches where the animal cannot depend on vision: for example in caves, in murky water and at night. Examples: electric eel,

46. In passive electrolocation, the animal senses the weak bioelectric fields generated by other animals and uses it to locate them. These electric fields are generated by all animals due to the activity of their nerves and muscles. A second source of electric fields in fish is the ion pumps associated with osmoregulation at the gill membrane. Examples: shark (can detect 0.5 V/m!), platypus, Guiana dolphin Electroreceptors in the head of a shark.

47. Recap Lecture 4

48. Today: Electric field lines Lightning rods Electric dipoles Microwave oven

49. Ways of Visually Representing an Electric Field Collection of vector arrows: Electric field lines: +

50. E ? 1. Electric field lines point in the direction of the (total) electric field at each point in space 2. Electric field lines start on charges and end on charges 3. Electric field lines cannot cross. Electric Field Line Model

51. 4. The number of field lines N coming out of or going into a charge is proportional to the magnitude of the charge |Q|, i.e., N |Q|. 5. The strength (magnitude) of the electric field at any place is proportional to the density of field lines there, i.e., N lines over all directions in 3-D. 2N lines over all directions in 3-D 2QQ E ( ) ( ) # of field lines area lines

52. + Collection of vector arrows: Electric field lines: Electric Dipole -

53. In 1947, Raytheon built the "Radarange", the first commercial microwave oven. It was almost 6 tall, weighed 750 lb and cost about US$5000 each. Uses microwave energy, usually at a frequency of 2.45 GHz from a magnetron How does a microwave oven heat? + + -- Uses dielectric heating: Many molecules (such as those of water) are electric dipoles High-frequency alternating electric field causes molecular dipole rotation within the food -> heating

54. A. (a) B. (b) C. (b) and (d) D. (a) and (c) E. (b) and (c) Consider the four field patterns shown. Assuming there are no charges in the regions shown, which of the patterns represent(s) a possible electrostatic field:

55. A. Same sign and 21 QQ . B. Same sign and 21 QQ . C. Opposite sign and 21 QQ . D. Opposite sign and 21 QQ . E. Opposite sign and 21 QQ . How are charges Q1 and Q2 related?

56. A B C At which of the labeled points is the electric field magnitude the largest? A. A B. B C. C D. A and C tie E. Same at all three points

57. If a proton were released from rest at point A, would the protons subsequent path follow the electric field line on which it starts? A. Yes B. No

58. A. B. C. D. E. Which best describes the path of the proton between the two plates with equal charge magnitudes but opposite signs?

59. At which point near the flat infinite uniform sheet of positive charge does the electric field have the greater magnitude? A B A. A B. B C. The field has the same magnitude at both points.

60. A flat infinite uniform sheet of positive charge is parallel to a flat infinite uniform sheet of negative charge. The magnitude of the surface charge density of both sheets is the same, i.e., . If E is the electric field magnitude due to the positive sheet alone, what is the electric field magnitude between the sheets? A. E B. 2E C. E2 D. Zero E. Not enough information.

61. A flat infinite uniform sheet of positive charge is parallel to a flat infinite uniform sheet of negative charge. The magnitude of the surface charge density of both sheets is the same, i.e., . If E is the electric field magnitude due to the positive sheet alone, what is the electric field magnitude to the right of the sheets? A. E B. 2E C. E2 D. Zero E. Not enough information.

62. How does a lightening rod work? Lightning: Atmospheric electrostatic discharge Path of ionized air starts from a negatively charged thundercloud When it approaches the ground, a conductive discharge (called a positive streamer) can develop from ground- connected objects whose tops are closest to the base of the thundercloud, such as trees and tall buildings. Lightning rod: Invented by Benjamin Franklin in 1749 Thundercloud attracts charge at top of rod Strong electric fields at top of rod ionizes nearby air molecules -> attracts and intercepts a strike that terminates near a protected structure

63. Recap Lecture 5

64. Today: Gauss Law

65. Conductors in Electrostatic Equilibrium An electric conductor has some mobile charges that are free to move in the conductor and along its surfaces. Electrostatic equilibrium means that charges are in static equilibrium. This means that there must be no net electric force on any mobile charge. 1. inside a conductor in electrostatic equilibrium. No! q elecF E If was in the conductor, then a mobile charge would be acted on by a net electric force , and would therefore have a nonzero acceleration and would therefore not be in equilibrium

66. 2. Any isolated charge on a conductor in electrostatic equilibrium can only be on its surfaces. 3. The excess charge on a conductor in electrostatic equilibrium is more concentrated in regions of greater curvature (no external electric field). No! E + If isolated (separated) charges were present in the conductor, then electric field lines would start or end on each charge, and would in there.0E + + + + + + + + + + F F F F sF sF Force component parallel to surface pushes surface charges apart

67. 4. just outside the surface of a conductor in electrostatic equilibrium must be perpendicular () to the surface. No! q elecF ||E E If had a component parallel () to the surface ( ), then a mobile charge on the surface would be acted on by a force , and would therefore have a nonzero acceleration and would not be in equilibrium. E 0|| E 0||elec EqF

68. Summary: Conductors in Electrostatic Equilibrium 1. inside 2. Excess charge can only be on its surfaces 3. Excess charge is more concentrated in regions of greater curvature 4. at surface must be perpendicular to surface

69. In each of the above cases, the conductors have charges that are equal in magnitude but opposite in sign. In each case, the positively charged conductor is the one on the right.

70. Recap Lecture 6

71. Today: Electric potential energy and potential

72. Consider a rectangular Gaussian surface surrounding a dipole that has 16 field lines emanating from its positively charged end. If you move the Gaussian rectangle around (anywhere in the plane), the field line flux through the rectangle: A. Always remains zero B. Varies between -32 and +32.3 C. Varies between -16 and +16 D. Is -16, zero, or 16 E. Other -+

73. x y A B a b A. Wb Wa B. Wb Wa C. Wb Wa If the charge is moved along path b how does the work done by the electric force compare with that done when the charge is moved along path a?

74. A. and B. and C. and D. and E. None of the above. x y A B There is a uniform electric field between the plates. An electron is moved from point A to point B. U Ue,B e,A 0 V VB A 0 U Ue,B e,A 0 V VB A 0 U Ue,B e,A 0 V VB A 0 U Ue,B e,A 0 V VB A 0 Which of the following is true?

75. Recap Lecture 7

76. Today: More on the electric potential Equipotential surfaces How to find the potential from the electric field How to find the electric field from the potential Potential of a point charge Transmission of nerve impulses

77. Equipotential surfaces: Examples Note: In reality, all of these are 3D! Uniform electric field Point charge Electric dipole Equipotential surface Field line

78. A. B. C. D. Cant tell A B C The isolated piece of metal (conductor) shown (in cross section) has a net charge and is in electrostatic equilibrium. Which of the following is true concerning the potential difference between points A and B? (Point B is inside the metal.) 0AB VV 0AB VV 0AB VV

79. A. B. C. D. Cant tell A B C The isolated piece of metal (conductor) shown (in cross section) has a net charge and is in electrostatic equilibrium. Which of the following is true concerning the potential difference between points A and C? 0AC VV 0AC VV 0AC VV

80. A. Yes B. No C. Cant tell The isolated hollow piece of metal (conductor) shown above (in cross section) has a net charge and is in electrostatic equilibrium. Is there an electric field anywhere in the hollow inside the metal? A B

81. An electron (q 0 B. Wel < 0 C. Wel = 0 A B 60 V 70 V 80 V 90 V

82. The graph shows the electric potential V as function of x. In which region has the x-component of the electric field the largest positive value? A. Region 1 B. Region 2 C. Region 3 D. Region 4 E. Region 5 V x1 2 3 4 5

83. Transmission of Nerve Impulses Axon: transmits nerve impulses In resting state: -70 mV potential of fluid inside relative to fluid outside (negative ions on inner surface of membrane and positive ions on outside) Nerve impulse changes the potential difference across the membrane (by sodium ion flow though membrane) to ~+40 mV Action potential propagates with 30 m/s down the axon ~20% of resting energy of human body goes into active pumping of sodium ions! V

84. Recap Lecture 8

85. Transmission of Nerve Impulses Axon: transmits nerve impulses In resting state: -70 mV potential of fluid inside relative to fluid outside (negative ions on inner surface of membrane and positive ions on outside) Nerve impulse changes the potential difference across the membrane (by sodium ion flow though membrane) to ~+40 mV Action potential propagates with 30 m/s down the axon ~20% of resting energy of human body goes into active pumping of sodium ions! V

86. EEG and ECG Electrocardiography (ECG or EKG) is a transthoracic (across the thorax or chest) interpretation of the electrical activity of the heart Detected by electrodes attached to the skin Measures potential difference (voltage) do to changes on the skin that are caused when the heart muscle depolarizes during each heartbeat Electroencephalography (EEG) is the recording of electrical activity along the scalp. Measures voltage fluctuations resulting from ionic current flows within the neurons of the brain.

87. Faradays Cage Enclosure formed by conducting material or by a mesh of such material. Blocks out external static electric fields Recall: E=0 inside a hollow conductor ! Shielding effect first observed by Benjamin Franklin in 1755

88. Today: Potential of a point charge Capacitors Energy density of the electric field

89. qq qq d d What is the potential at the center of the square? Take V 0 at infinity. A. B. C. D. 2 0 center 8 4 1 d q V d q V 2 8 4 1 0 center d q V 4 4 1 0 center 0center V

90. Q Q If the charge on both metal plates (Q) were doubled, what would happen to the magnitude E of the uniform electric field between the plates? A. Decrease by a factor of 1/4. B. Decrease by a factor of 1/2. C. Stay the same. D. Increase by a factor of 2. E. Increase by a factor of 4.

91. Q Q If the charge on both metal plates (Q) were doubled, what would happen to the potential difference (voltage) between the plates? A. Decrease by a factor of 1/4. B. Decrease by a factor of 1/2. C. Stay the same. D. Increase by a factor of 2. E. Increase by a factor of 4.

92. V When the plates are moved apart, what happens to the voltmeter reading? A. Goes up. B. Goes down. C. Stays the same.

93. V When the plates are moved apart, what happens to the magnitude of the charge on each plate? A. Goes up. B. Goes down. C. Stays the same.

94. When the plates are moved apart, what happens to the voltmeter reading? A. Goes up. B. Goes down. C. Stays the same. V

95. Recap Lecture 9

96. Touch Screens Technologies: Infrared of optical Touch Capacitive Touch touching the screen surface results in a distortion of the screen's electrostatic field, measurable as a change in capacitance Resistive Touch Technology Surface Acoustic Wave

97. Today: Energy density of the electric field Dielectrics Electric current Electrical resistance

98. Energy stored in a Capacitor / Electric Field

99. 10 V 1 F 2 FWhich capacitor stores more charge? A. 1 F B. 2 F C. Both store the same charge

100. Vbatt C1 C2 Vbatt Ceff What should be the value of Ceff in terms of C1 & C2 so that the battery delivers the same charge in both circuits? Capacitors in Parallel

101. Which capacitor stores more charge? A. 1 F B. 2 F C. Both store the same charge 10 V 1 F 2 F

102. Vbatt Ceff Vbatt C1 C2 What should be the value of Ceff in terms of C1 & C2 so that the battery delivers the same charge in both circuits? Capacitors in Series

103. Dielectrics and Electric Fields

104. Moving Charges: Electric Current

105. Recap Lecture 10

106. Today: Electric current Current density Electrical resistance

107. Consider a beam of protons, all moving with constant velocity . If n is the number of protons per unit volume in the beam, how many protons pass through the cross sectional area A in time t ? v A. nAt B. n /(Avt) C. nAvt D. nAv /t A v

108. Consider a beam of protons (charge e), all moving with constant velocity . n is the number of protons per unit volume in the beam. What is the electric current carried by the beam? v A. 0 B. nevA C. nev D. evA A v

110. Today: Electrical resistance Resistivity and conductivity

111. Joule Heating: Running current through a resistance creates heat, in a phenomenon called Joule heating. In this picture, a cartridge heater, warmed by Joule heating, is glowing red hot.

112. band #1 is first significant figure of component value (left side) band #2 is the second significant figure band #3 is the decimal multiplier band #4 if present, indicates tolerance of value in percent (no color means 20%) Electronic color code Used to indicate the values of electronic components very commonly for resistors, but also for capacitors, inductors 100 kOhm = 10*1x104

113. R1 R2 R R1 2 Which resistor has the greater current going through it? A. R1 B. R2 C. The current through both resistors is the same V bat

114. R1 R2 R R1 2 Which resistor has the greater voltage (magnitude of potential difference) across it? A. R1 B. R2 C. The voltage across both resistors is the same V bat

115. R1 R2 3R Reff What should be the value of Reff in terms of R1, R2, & R3 so that the same current flows in both circuits? Resistors in Series V bat V bat

117. Today: Pumping charges:emf RC circuits

118. R1 R2 3R Reff What should be the value of Reff in terms of R1, R2, & R3 so that the same current flows in both circuits? Resistors in Series V bat V bat

119. R1 R2 R R1 2 Which resistor has the greater current going through it? A. R1 B. R2 C. The current through both resistors is the same V bat

120. R1 R2 R3 Reff What should be the value of Reff in terms of R1, R2, & R3 so that the same current flows in both circuits? Resistors in Parallel V bat V bat

121. E A B C D Which resistors are in series? A. A and B B. A and C C. A and E D. B and D E. Both answers C and D above

122. E A B C D Which resistors are in parallel? A. A and B B. A and C C. A and E D. C and D E. No pair listed above

123. Potential electric energy is used (converted to other forms of energy) in the devices of the circuit q q Potential energy Emf device pumps charges to higher potential energy

124. Ideal emf device Has no internal resistance. Real emf device Has internal resistance r. R r R When a load resistance R is connected to the real emf device, what is the potential difference across its terminals? A. B. 0 .C. R r .D. Rr R .E. Rr r

125. Converts chemical energy into electrical energy Anode (negative terminal) is made of zinc powder Cathode (positive terminal) is composed of manganese dioxide Electrolyte is potassium hydroxide Standard Alkaline Batteries: + pole - pole e- e- At potential V ~ 1.5V At potential V ~ 0V

126. RC circuit: Charging and discharging of a capacitor R C b a At time t 0 move the switch to position a. i i i i Current i begins to flow to charge the capacitor. i into the upper plate of the capacitor always equals i out of the lower plate even though no charge flows across the gap between the plates.

127. R C b a At time t 0 the switch is moved to position a. i i i i After a very long time what will be the voltage on the capacitor? A. 0 B. iR C. D. V, the voltage will keep increasing as long as the switch is at position a.

128. Recap Lecture 13 Matthias Liepe, 2012

129. Today: More on RC circuits Magnets and magnetic field

130. RC circuit: Charging R C a At time t 0 the switch is moved to position a. i i i i

131. R C b a The switch has been at position a for a very long time. i i Current i begins to flow to discharge the capacitor. At time t 0 move the switch to position b. RC circuit: Discharging

132. R C b i i At time t 0 the switch is moved to position b. RC circuit: Discharging

133. 0 20 40 60 80 100 120 0 50 100 150 200 250 Time t (s) Currenti(mA) What is the approximate value of the time constant for this decay of electric current from a discharging capacitor in a simple RC circuit? A. ~25 s B. ~35 s C. ~50 s D. ~100 s E. ~250 s

134. 0 20 40 60 80 100 120 0 50 100 150 200 250 Time t (s) Currenti(mA) Approximately, what was the discharging capacitors initial charge at time t = 0 ? A. 1.2 C B. 3.0 C C. 6.0 C D. 12 C E. 18 C

135. Charging 0 1 2 3 4 5 6 0 50 100 150 200 250Time t Chargeq The graph shows the electric charge on a charging capacitor in a simple RC circuit. At time t =2 , how much charge is on the capacitor? qf A. 0.14 qf B. 0.37 qf C. 0.63 qf D. 0.79 qf E. 0.86 qf

136. Magnetic Fields and Forces A. To the geographic north pole B. To a point near the geographic north pole C. To the geographic south pole D. To a point near the geographic south pole The Earths magnetic field near the surface can be approximated by the field of a bar magnet. In which direction would the magnetic north pole of Earths magnet point?

137. Magnetic Fields and Forces

138. How can we detect a magnetic field B?

139. Recap Lecture 14 Matthias Liepe, 2012

140. Today: Magnetic field Magnetic field lines Charge moving in a uniform B-field Particle accelerators: The cyclotron and synchrotron

141. A beam of electrons traveling directly towards you produces a bright spot when it hits a CRT screen. S N If a magnet with its north pole facing down is brought near the beam from above, which way will the spot on the screen move? ? A. B. C. D. E. It wont move.

142. Which way does FB point?

143. Right Hand Rule: Must use your right hand! The figure below shows the force for a positive charge, i.e. q>0!!

144. Right Hand Rule: Must use your right hand!!! FINGERS of the right hand point in the direction of the FIRST vector (v) in the cross product, then adjust your wrist so that you can bend your fingers (at the knuckles!) toward the direction of the second vector (B); extend the thumb. If charge is positive the force is in direction that the thump points! If charge is negative, the force is opposite to direction that the thump points! v B Fif q>0 Fif q Magnetic field at Center of a Wire Loop: -> Magnetic field at Center of a circular Arc of Wire: P i R Circumference= 2 R Arc length = R

190. y i i R Pr What is the direction of the magnetic field, , at point P due to the current at ? PBd sd A. B. C. (out of) D. (into) E. Cant tell ds

191. 0 y i i R jdysd Pr Example 2: Magnetic field due to a current in a long straight wire:

192. i R P i 1 2 3 What is the direction of the magnetic field, , at point P due to the current in wire section 1? 1P,B A. (out of) B. (into) C. D. E. No field at P due to section 1.

195. i R P i 1 2 3 Current-carrying wire: What is the total magnetic field at point P due to the current in wire? PB

196. A. B. C. D. What is the direction of the magnetic field at wire #2 due to the current in wire #1? Consider two long wires running in parallel with current going through them in the directions shown below:

197. A. B. C. D. What is the direction of the magnetic force on wire #2 by the field caused by wire #1? Consider two long wires running in parallel with current going through them in the directions shown below:

198. P ii R Arc length = R Matthias Liepe, 2012 Recap Lecture 18

199. Today: Amperes law Applications of Amperes law Straight wire Solenoid

200. Ex.: Calculate for a circular path centered around a long straight wire: i R integration path sd What is the component of along the direction of ?B sd A. Bs 0i(2R). B. Bs 0i(2R). C. 0. D. It depends on where is along the path. E. Not enough information. sd

201. i R integration path sd sdB Ex.: Calculate for a circular path centered around a long straight wire:

202. Amperes law: where ienc,net is the net current enclosed by the closed path of integration and is the angle between B and ds. ienc,net i1 i2. netenc,0||cos idsBdsBd sB i1 (out of) i2 (into) integration path Use a right-hand rule to assign or signs to enclosed currents.

203. current enclosed by the closed path: current must pierce through imaginary surface that is completely bounded by the closed integration path right-hand rule to find sign of current: Curl fingers of your right hand along the direction of the closed integration path. Then a positive current will run in the general direction of your thumb, while a current which runs in the opposite direction is negative. Integration path direction Positive current direction

204. Applications of Amperes law: In certain cases, Amperes law can be used together with symmetry arguments to find an unknown magnetic field. - Magnetic field by a long, straight wire - Magnetic field by a long solenoid

205. Which configuration of magnetic field along the integration path can be correct (use symmetry arguments)? r r r B B B A. B. C. D. None of the above. Consider a long, straight Wire:

206. Applications of Amperes Law: Magnetic Field outside of a Long, straight Wire

207. A. B. C. 0 D. E. Cant tell. Consider two long straight current-carrying wires as shown below: What is the value of for the path shown? sdB 0 i2 0 i 0 i

208. A. B. C. 0 D. E. Cant tell. Consider two long straight current-carrying wires as shown below: What is the value of for the path shown? sdB 0 i2 0 i 0 i

209. R Wire, shown in cross section, carries a current i out of () the screen. Assume that the magnitude of the current density is constant across the wire. r integration path Because of the cylindrical symmetry, the only coordinate that B can depend on is r. Applications of Amperes Law: Magnetic Field inside of a Long, straight Wire

210. R Wire, shown in cross section, carries a current i out of () the screen. Assume that the magnitude of the current density is constant across the wire. r A. i B. i C. ir 2R 2 D. ir 2R 2 E. irR Magnetic Field inside of a Long, straight Wire integration path

211. Magnetic field due to a circular current-carrying loop: i (out of) i (into)

212. i (out of) i (into) Applications of Amperes Law: Magnetic Field inside a Solenoid

213. i (out of) i (into) integration path h d c a b Magnetic Field inside a Solenoid

214. Matthias Liepe, 2012 Recap Lecture 19

215. Today: Magnetic materials Change in magnetic flux and Faradays law of induction Lenzs law

216. Magnetic Materials Ferromagnetic: Examples: Iron, nickel Divided into regions (domains) in which atomic magnetic dipoles line up If placed in an external magnetic field: dipoles of domains line up in direction of magnetic field -> material develops a strong magnetic dipole moment in direction of the applied external magnetic field The dipole moment alignment (magnetization) partially persists when the external field is removed -> permanent magnet

217. Thats why a magnet sticks to a steel refrigerator door S N N

218. Example: Hard disk drive A hard disk drive records data by magnetizing a thin film of ferromagnetic material on a disk.

219. Diamagnetic: Atoms have no permanent dipole moments, but weak magnetic dipole moments are produced in the atoms when placed in an external magnetic field ->Create a very weak magnetic dipole field in opposition to an externally applied magnetic field Dipole moments and net field disappear when external magnetic field is removed Paramagnetic: Atoms have permanent dipole moments, but are randomly oriented When placed in an external magnetic field, dipoles partially align in direction of the field ->Create a net magnetic dipole field in direction of the externally applied magnetic field Alignment and net field disappear when external magnetic field is removed

220. Example: Levitation of a Frog on a strong Magnetic Field A live frog levitates inside a 32 mm diameter vertical bore of a solenoid in a magnetic field of about 16 T. Why? Diamagnetism of the frog Magnetic dipole moment of frog opposes Bext -> repulsive force!

222. Today: More on magnetic induction: Lenzs law Inductors and their inductance

223. Lenzs law: To determine the direction of the induced current in the loop, use: 1. An induced current has a direction such that the magnetic field due to the induced current opposes the change in the magnetic flux that induces the current. Same as saying:: 2. An induced emf acts to oppose the change that produces it.

224. Another way to determine the direction of the induced current in the loop: Select the positive direction of the area vector for the given loop (this vector is always normal to the loop!) Determine the direction of positive () emf in the loop according to a right-hand rule (point thump in positive direction of the area vector; finger then point in positive direction of the emf). Calculate the induced emf with Faradays law. The sign ( or ) of the induced emf calculated then tells the direction of the induced emf. Lenzs law:

225. 3 Examples

226. Example 1: B uniformspatially loop of wire of resistance R A Suppose that B is changing with time t according to B(t) kt B0, where k and B0 are positive constants. A. 0 B. (kt B0)A C. kAt D. kA E. kA What is the emf induced in the loop?

227. loop of wire of resistance R A Suppose that B is changing with time t according to B(t) kt B0, where k and B0 are positive constants. A. Clockwise B. Counterclockwise C. There is no induced current D. Cant tell Example 1: B uniformspatially What is the direction of the induced current?

228. Example 2: Wire loop rotating counterclockwise with constant angular speed in a uniform magnetic field: B uniformSide view: A At time t 0, 0. What is the magnetic flux B through the loop at some time t 0? A. BAsin(t) B. BAcos(t) C. 0

229. At the instant shown above, what is the emf induced in the loop? A. 0 B. BA C. BA D. Cant tell. Example 2: Wire loop rotating counterclockwise with constant angular speed in a uniform magnetic field: B uniformSide view: A

230. At the instant shown above, what is the direction of the induced current in the loop as seen by an observer directly below the loop? A. Clockwise B. Counterclockwise C. There is no induced current D. Cant tell Example 2: Wire loop rotating counterclockwise with constant angular speed in a uniform magnetic field: B uniformSide view: A

231. B v At the instant shown above, what is the direction of the induced current in the metal loop? A. Clockwise B. Counterclockwise C. There is no induced current D. Cant tell Example 3:

232. B v At the instant shown above, what is the direction of the net magnetic force on the metal loop? A. B. C. D. E. The net magnetic force on the loop is zero. Example 3:

233. Inductors and Inductance L:

235. Today: Inductors and their inductance RL circuits Energy density of a magnetic field

236. Inductors and Inductance L:

237. i (increasing) RL circuit: Rise of current R L b a At time t 0 move the switch to position a. i i i Current i begins to flow but the self-induced emf L in the inductor L opposes the rise in current. -> Current starts out at 0 at t=0 and then increases until it approaches a steady state value asymptotically. L

238. i (t)? R L b a At time t 0 move the switch to position a. i i i After a very long time what will be the magnitude of the steady state current in the circuit? L A. 0 B. |L|R C. R D. ( |L|)/R E. Both answers C & D above.

239. At time t 0 move the switch to position a. i (increasing) R L a i i i L RL circuit: Rise of current

240. RL circuit: Rise of current

241. i (decreasing) R L b i i i RL circuit: Decay of current The switch has been in position a for a very long time. At time t 0 move the switch to position b. Current i begins to decrease, but the self-induced emf L in the inductor L slows down the decease in current. -> Current starts out at the equilibrium value, and then decays to zero over time.

242. i (decreasing) R L b a i At time t 0, switch to position b using a make- before-break switch. L RL circuit: Decay of current

243. RL circuit: Decay of current

244. Matthias Liepe, 2012 Recap I Lecture 22

245. Recap II

246. Today: Energy density of a magnetic field Alternating current and power Transmission lines and transformers Ideal LC circuit

247. i (increasing) R L b i i i L RL circuit: Power supplied and dissipated in the circuit

248. At time t 0 the switch is moved to position a. i R L b a i i i L After t 0, how does the power delivered to the inductors magnetic field vary with time? A. It starts low & steadily increases. B. It starts high & steadily decreases. C. It starts low, then increases until it reaches a peak, & then decreases. D. Its constant.E. It oscillates.

249. Why is power transmitted at very high voltages in power transmission lines (several 100,000 volts)? A. Because it reduce the energy lost in long- distance transmission B. Because it maximized the power that can be transmitted C. Because it is easier to generate high voltages

250. Alternating current (ac):

251. Electrical transmission system:

253. Today: Alternating current and power Transformers Ideal LC circuit RLC circuit: damping and driven

254. Transformer: Iron core ~ R Primary Secondary Vp Vs Np turns Ns turns The iron core ensures that the B per turn is the same in both the primary & secondary windings.

255. Iron core ~ R Primary Secondary Vp Vs Np turns Ns turns Transformer:

256. Ideal LC circuit (no resistance)

257. LC The capacitor starts with charge Q. At time t 0 the switch is closed. Let T represent the period of the circuit oscillations. What is the charge on the capacitor at time T2? A. 0 B. Q2 C. Q2 D. Q E. Q

259. Today: RLC circuit: damping and driven Another look at Faradays law Next time: Maxwells equations

260. Ideal LC circuit (no resistance): LC The capacitor starts with charge q Q 0 with the polarity shown. At time t 0 the switch is closed and current i dqdt flows in the circuit. -3 0 3 0 1 2 3 4 Time t Currenti +i m - i m T 2T A B C D Which of the labeled points correspond(s) to no voltage across the inductor? A. A B. B C. C D. D E. Both A & C A graph of i versus t is shown below.

261. Which of the labeled points correspond(s) to no voltage across the capacitor? LC The capacitor starts with charge q Q 0 with the polarity shown. At time t 0 the switch is closed and current i dqdt flows in the circuit. A graph of i versus t is shown below. -3 0 3 0 1 2 3 4 Time t Currenti +i m - i m T 2T A B C D A. A B. B C. C D. D E. Both A & C

262. -3 0 3 0 1 2 3 4 Time t Currenti +i m - i m T 2T A B C D Which of the labeled points correspond(s) to charge +Q on the capacitor? LC The capacitor starts with charge q Q 0 with the polarity shown. At time t 0 the switch is closed and current i dqdt flows in the circuit. A graph of i versus t is shown below. A. A B. B C. C D. D E. Both A & C

263. Which of the labeled points correspond(s) to counterclockwise current flow in the circuit? -3 0 3 0 1 2 3 4 Time t Currenti +i m - i m T 2T A B C D LC The capacitor starts with charge q Q 0 with the polarity shown. At time t 0 the switch is closed and current i dqdt flows in the circuit. A graph of i versus t is shown below. A. A B. B C. C D. D E. Both A & C

264. RLC circuit: i (increasing in magnitude) LC i R

265. Driven RLC circuit: L C R ~ )cos()( dm tt Current will oscillate at the driving frequency: fd d(2) Maximum current amplitude when driving frequency matches natural frequency of circuit: 2 1 0d LC ff )(resonance

266. B uniformspatially integration path , dt d sdE B - When Faradays law, is applied to the circular integration path, which best describes Es, the component of the electric field along the direction of ?sd A. Es 0 B. Es 0 C. Es 0 D. Es depends on where is along the integration path.sd The magnetic field is confined to the cylindrical region shown and is spatially uniform but its magnitude is increasing with time.

267. B uniformspatially , dt d sdE B - When Faradays law, is applied to the circular integration path, which best describes Es, the component of the electric field along the direction of ?sd A. Es 0 B. Es 0 C. Es 0 D. Es depends on where is along the integration path.sd The magnetic field is confined to the cylindrical region shown and is spatially uniform but its magnitude is increasing with time. integration path

269. Recap II

270. Today: Maxwells equations Electromagnetic waves Polarization

271. Which set of expressions describes the electric field of an EM wave that travels in the -y direction and is polarized along the z direction? A. E E kz ty m sin( ) , Ex 0, Ez 0. B. E E kz ty m sin( ) , Ex 0, Ez 0. C. E E ky tz m sin( ) , Ex 0, Ey 0. D. E E ky tz m sin( ) , Ex 0, Ey 0. E. None of the above.

272. Which set of expressions describes the magnetic field of an EM wave whose electric field is given by , , ?E E kz ty m sin( ) Ex 0 Ez 0 A. B E c kz tx m sin( ) , By 0, Bz 0. B. B E c kz tx m sin( ) , By 0, Bz 0. C. B E c kz tx m cos( ) , By 0, Bz 0. D. B E c kz ty m sin( ) , Bx 0, Bz 0. E. None of the above.

273. V: Sources of EM waves: Accelerating charges (changing currents) radiate EM waves. Example: Electric dipole antennas: ~ Transmitter Receiver

274. VI: Spectrum of EM waves: Note: These are all electromagnetic waves! Only difference is frequency (wavelength)!

276. Recap II

277. Today: More on electromagnetic waves Spectrum Energy transport Polarization Why is the sky blue, and why does it turn dark blue at 90 degrees from the sun?

278. V: Sources of EM waves: Accelerating charges (changing currents) radiate EM waves. Example: Electric dipole antennas: ~ Transmitter Receiver

279. VI: Spectrum of EM waves: Note: These are all electromagnetic waves! Only difference is frequency (wavelength)!

280. A B The electric dipole antenna of the microwave transmitter is vertical. Which orientation of the metal grill will allow the highest transmission of microwaves? A. A B. B C. Both will have about the same transmission.

281. The metal grill acts as a polarizing filter for microwaves. Transmission direction of the metal grill. Textbook representation of a polarizing filter (sheet) with a vertical polarizing (transmission) direction. Be careful to distinguish the polarizing direction of a filter from its actual physical shape.

282. It is desired to rotate the plane of polarization of a plane- polarized EM wave by 90 using ideal polarizing filters. What minimum number of such ideal polarizing filters, with equal angular spacing between successive filters, would be needed to do this if the intensity of the final transmitted wave is to be 50% or more of the original waves intensity? A. 2 B. 3 C. 4 D. 5 E. It cant be done this way.

284. Today: Polarization of EM waves Why is the sky blue, and why does it turn dark blue at 90 degrees from the sun? Reflection and refraction Snells law

285. Polarization of Light by Scattering Arrows () show E oscillation directions in light. Unpolarized light is a mixture of all polarizations. Bold arrows () show electric charge (dipole) oscillations in molecules due to E oscillations from incident light. These charge oscillations capture incident light energy and re- radiate or scatter it in all directions with polarizations as indicated.

286. Blue light is scattered more than visible light of other colors (lower frequencies). Thats why the sky is blue Photo without polarization filter Photo taken with polarization filter Notice that the sky turns dark blue at 90 degrees from the sun!

287. An unpolarized beam of light is directed into the side of an aquarium containing cloudy water. Light scattered by the cloudy water out of the front of the aquarium is to be observed through a polarizing filter. Which orientation of the transmission direction of the filter will transmit the most light? A. Horizontal. B. Vertical. C. 45 to horizontal. D. All orientations will transmit the same amount of light.

288. Geometrical Optics

289. Reflection and Refraction incident refracted reflected Water: n=1.33 Air: n=1.00 Interface between two materials

290. Reflection and Refraction

291. Refraction: Example

293. Today: Reflection and Refraction Polarization Chromatic dispersion Rainbows Images

294. An inferior mirage on the Mojave Desert (image seen is under the real object) A inferior mirage occurs when the air near the ground is much warmer than the air above In this case the light rays are bent up and so the image appears below the true object

295. A superior mirage occurs when the air below the line of sight is colder than that above (temperature inversion) In this case the light rays are bent down and so the image appears above the true object An superior mirage (image seen is above the real object)

296. A. B. C. D. It depends on the thickness of medium 2. 1 A,3 3n 1n 2n 1n 3n 321 nnn . 1 A B The angle is the same in both cases A and B. For case B, how does the angle that the ray makes with a normal to the interfaces when its in the medium with refractive index compare with ? AB ,3,3 AB ,3,3 AB ,3,3 3n A,3 B,3 1

297. Application of total internal reflection: Optical fibers Optical fibers typically include a transparent core surrounded by a transparent cladding material with a lower index of refraction. Light is kept in the core by total internal reflection. This causes the fiber to act as a waveguide.

298. A right-angle isosceles prism can be used to redirect a high-power laser beam that would destroy a normal silvered mirror. As shown in the figure, the beam enters the prism normal to one of its equal sides. In order for this to work, the refractive index of the prism must be greater than a particular value. What is this value? Laser beam Air (nair 1.00) A. 2.00. B. 1.73. C. 1.41. D. 1.33. E. 1.15.

299. Interface Normal () to interface n1 n2 Incident unpolarized ray Reflected plane- polarized ray Refracted partially- polarized ray B B 2 In general, light reflected from an interface is partially polarized. At one particular incidence angle B (the Brewster angle), the reflected light is completely polarized. For light incident at the Brewster angle, the reflected & refracted rays are to each other. E Polarization in Reflection and Refraction

300. Interface Normal () to interface n1 n2 Incident unpolarized ray Reflected plane- polarized ray Refracted partially- polarized ray B B 2 E .902B )sin()sin( 22B1 nn )90sin( B2 n .)cos( B2 n .)tan( 1 2 B n n For Brewster angle B

301. Interface Normal () to interface n1 n2 ( n1) Incident white light Reflected white light Refracted light 1 1 2,red Refractive index n depends on the wavelength (or frequency f) of the light. Generally n is greater for a shorter wavelength. -> In general, n (violet) > n (red) 2,violet Chromatic dispersion:

302. Incident white light in air Screen White light is incident on the prism as shown. Which color of light will hit higher () on the screen? A. Violet B. Blue C. Red Example: Prism

303. Rainbows: Secondary rainbow:

304. Images: Light rays diverge from an object in all directions. We see the object because some of these rays enter our eyes We perceive the rays as coming straight from the location of the object / image. Real images: Perceived location of image is actually a point of convergence of the rays of light that make up the image Virtual images: Rays only appear to diverge from a point on the image.

305. Real image Virtual image O I Real rays do converge at location of image (can put a screen at location of image and form the image) Rays only appear to converge at location of image (your brain thinks the image is at this location, but it is not real)

306. Image formation by a plane (flat) mirror: Convention: i Population inversion for Ne Energy Helium states Neon states Ground state Excitation via collisions metatable He-Ne collisions Rapid decay photon

413. Startup of a LASER Pumping produces a population inversion, i.e. more atoms in are in an excited state then in the ground state. Excited atoms emit photons; initially in random directions. Photons cause other exited atom to emit via stimulated emission. Photons parallel to axis reflect from mirrors. Reflected photons stimulate further emission by excited atoms. -> amplification in each pass though the laser medium.

414. Particle waves = h/p : Order of Magnitude Estimate

415. An electrons kinetic energy K is the same as the energy Eph of a photon with 10 nm associated wavelength. How does the electrons de Broglie wavelength compare with the wavelength associated with the photon (hc = 1240 eV nm; E0,e-=511 keV)? A. electron photon. B. electron photon. C. electron photon. D. Not enough information.

416. Davisson-Germer Experiment (1925): Scattering of low energy electrons by a crystal surface (1/) 1 Evidence for de Broglies Particle Waves:

417. G. P. Thompsons Experiment: Diffraction of 10 40 keV electrons by a thin polycrystalline foil polycrystalline film Bragg condition satisfied for any given reflecting plane concentric circles 0.1 =10-11 m thin foil screen

418. Electron diffraction by polycrystalline aluminum Laue pattern of electron diffraction by a single crystal (Courtesy of Prof. Y. Soejima, Dept. of Physics, Kyushu Univ.)

419. 2-slit Interference of Electrons

420. Diffraction of Neutrons = several down to

sem5 em cornell edu phys2208 lecture01 41

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