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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
109. Recap Lecture 11
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
116. Recap Lecture 12
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.
193. 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 2? 2P,B A. (out of)
B. (into) C. D. E. No field at P due to section 2.
194. 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 3? 3P,B A. (out of)
B. (into) C. D. E. No field at P due to section 3.
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!
221. Matthias Liepe, 2012 Recap Lecture 20
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:
234. Matthias Liepe, 2012 Recap Lecture 21
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:
252. Matthias Liepe, 2012 Recap Lecture 23
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
258. Matthias Liepe, 2012 Recap Lecture 24
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
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)!
275. Matthias Liepe, 2012 Recap I Lecture 26
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.
283. Matthias Liepe, 2012 Recap Lecture 27
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
292. Matthias Liepe, 2012 Recap Lecture 28
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.)