Problem 1 (25 points)


 Ella Hunt
 1 years ago
 Views:
Transcription
1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2012 Exam Three Solutions Problem 1 (25 points) Question 1 (5 points) Consider two circular rings of radius R, each perpendicular to the axis of symmetry, with their centers located at z = ± l / 2. There is a steady current I flowing in the same direction around each coil, as shown in the figure below. A magnetic dipole, with dipole moment µ = µî where µ is a positive constant with units A m 2, is placed on the symmetry axis, at the position z = l / 4. The dipole will a) experience no force and no torque. b) align itself to point in the positive z direction and experience a force in the positive z direction. c) align itself to point in the positive z direction and experience a force in the negative z direction. d) align itself to point in the negative z direction and experience a force in the positive z direction. e) align itself to point in the negative z direction and experience a force in the negative z direction. f) align itself to point in the positive z direction but feel no force. g) align itself to point in the negative z direction but feel no force. The correct answer is b and f accepted as correct. 1
2 Question 2 (5 points) A square wire loop rotates in the direction shown (see sketch) in a magnetic field directed to the right. At the instant shown, when 0 < θ < π / 2, which of the figures below best describes the direction of current in the square wire loop and the direction of the magnetic torque on the square wire loop? The correct answer is c. At the instant shown the flux is increasing (in the ˆn direction) so there is a clockwise induced current to oppose that change. Therefore the magnetic dipole vector points in the negative ˆndirection. The torque τ = µ B ext is therefore in the positive z direction. 2
3 Question 3 (5 points) A coil of wire with resistance R defines an open surface whose normal d A points upward, as shown in the sketch. The coil is below a magnet whose magnetic field lines and directions are shown in the figure above. If positive current is defined as counterclockwise as viewed from the top, and if we ignore any selfmagnetic field generated by the induced current, then as the coil moves from well below the magnet to well above that magnet, the induced current through the coil will look like (a) (b) (c) (d) The correct answer is c. 3
4 Question 4 (5 points) The figure above on the left shows a side view of a section of a very long solenoid with radius R carrying current I with magnetic field pointing up at time t. The figure above on the right shows a top view of the electric field E inside the solenoid at a radius r and the direction of the magnetic field B at time t. In the solenoid, the current I is a) increasing in time. b) constant. c) decreasing in time. d) cannot tell without more information. The correct answer is c. 4
5 Question 5 (5 points) A very long solenoid consisting of n turns per unit length has radius R and length d ( d >> R ). Suppose the current running through the solenoid is doubled keeping all the other parameters fixed. You may neglect edge effects. Which of the following is true? a) The energy stored in the magnetic field and the selfinductance remain the same. b) The energy stored in the magnetic field doubles and the selfinductance remains the same. c) The energy stored in the magnetic field is four times as large and the selfinductance remains the same. d) The energy stored in the magnetic field remains the same and the selfinductance doubles. e) The energy stored in the magnetic field remains the same and the selfinductance is four times as large. f) None of the above. The correct answer is c. 5
6 Problem 2 (25 points) NOTE: YOU MUST SHOW WORK in order to get any credit for this problem. Make it clear to us that you understand what you are doing (use a few words!) A very long coaxial cable consists of a solid cylindrical inner conductor of radius a, surrounded by a concentric cylindrical conducting shell of inner radius b and outer radius c. The inner conductor has a nonuniform current density J inner = αr ˆk (pointing to the left in the figure just below) where α is a positive constant with units A m 3. The outer conductor has a uniform current density J outer = β ˆk where β is a positive constant with units A m 2. The conductors carry equal and opposite currents of magnitude I 0. a) Find expressions for α and β in terms of a, b, c, and I 0. For current through 0 < r < a, For current through b< r < c, a J ˆn da = I o = 2πr dr αr S 0 ( ) c J ˆn da = I o = 2πr dr ( β ) = βπ c 2 b 2 S b = 2πα 3 a3 α = 3 I o 2π a 3 ( ) β = I o π c 2 b 2 ( ) b) Determine the magnitude and direction of the magnetic field for the regions (i) r < a, (ii) a < r < b, (iii) b < r < c, (iv) and r > c. For each region, redraw the coaxial cable clearly indicating your choice of Amperian loop and associated parameters. For r < a, loop is circle of radius r < a, and 6
7 B d s = 2πrB θ = µ 0 J ˆn da closed path = µ 0 2π S r 0 r d r α r ( ) = 2π 3 αr 3 2 ˆ αr B = θ µ where ˆθ is a unit vector oriented counterclockwise. 0 3 For a<r < b, loop is circle of radius a<r < b, and B d s = 2πrB θ = µ 0 J ˆn da closed path where ˆθ is a unit vector oriented clockwise. = µ 0 I 0 S ˆ µ B = θ 2π r 0I o For b<r < c, loop is circle of radius b<r < c, and closed path B d s = 2πrB θ = µ 0 I o 1 β 2π I o ˆ µ 0I o β B = θ 1 π 2π r Io r b r d r = µ I 1 β π r 2 b 2 0 o ( ) I o 2 2 ( r b ) where ˆθ is a unit vector oriented counterclockwise. This can be written using the results above as For c<r, loop is circle of radius c<r, and 2 2 ( c r ) 2 2 ( ) ˆ µ 0Io B = θ 2π r c b B d s = 2πrB θ = 0 closed path c) Make a graph of the magnitude of the magnetic field as a function of the distance r from the central axis of symmetry. Clearly label each axis with any relevant values. 7
8 µ 0I The graph is a concave upward parabola from 0 to a, rising to a value of o at r = a. 2π a µ 0I Then it goes as inverse r from a to b, decreasing to o at r = b. Then it decreases from 2π b its value at r = b to 0 as we move from b to c. It is zero thereafter. 8
9 Problem 3 (25 points) NOTE: YOU MUST SHOW WORK in order to get any credit for this problem. Make it clear to us that you understand what you are doing (use a few words!). Consider a slab that is infinite in the x and z directions that has thickness d in the y direction. The slab has a time varying current with the current density as a function of time given by the following expression: 0; t 0 J = (J e t / T ) ˆk; 0 t T, J e ˆk; T t where J e is positive constant with units of amps per square meter and T is a constant with units of seconds. a) Find the direction and magnitude of the magnetic field for the interval 0 t T in the regions: (i) 0 y d / 2 ; (ii) y d / 2. Clearly show all your work. Answers without justification will receive no credit. 0 y d / 2 : By symmetry we argue that the field is zero at y = 0. We take an Amperean loop whose bottom is at y = 0 and whose top is at 0 y d / 2, of width w. We have closed path B d s = wb x = µ 0 J ˆn da = µ 0 wy(j e t / T ) B = ˆxµ 0 y(j e t / T ) S d /2 y: We take an Amperean loop whose bottom is at y = 0 and whose top is at d /2 y, of width w. We have closed path B d s = wb x ( y) = µ 0 J ˆn da = µ 0 w d 2 (J e t / T ) B = ˆxµ 0 S d 2 (J e t / T ) 9
10 Suppose a square conducting loop with resistance R, and side s is placed in the region y d / 2, at a height h above the top of the slab oriented as shown in the figure below. What is the induced current in the square loop for the time interval 0 t T? Draw the direction of the induced current on the figure. The direction of the current is counterclockwise when looking from the right. d Φ d d d = = dt dt dt µ 2 1 dφ d Js = =. R dt 2 RT 2 B 2 2 e s 0 ( Je t/ T) s I µ 0 b) What is the direction and magnitude of the force due to the induced current on the square loop during the time interval 0 t T? What is the direction and magnitude of the torque due to the induced current on the square loop during the time interval 0 t T? Since the loop is sitting in a uniform field, the force is zero. Since the loop has a magnetic dipole moment antiparallel to the magnetic field, the torque τ = µ B ext is also zero. 10
11 Problem 4 (25 points) NOTE: YOU MUST SHOW WORK in order to get any credit for this problem. Make it clear to us that you understand what you are doing (use a few words!). A stretchable and flexible conducting band in the shape of a circle with radius r(t) has constant resistance R. It sits in a uniform magnetic field B that is directed out of the page (see figure). External agents distributed uniformly over the circumference of the ring exert radial outward forces that cause the ring to expand at a constant speed from radius a to a larger radius b over a time interval 0 t T, where T is a constant with units of seconds. Let v = dr / dt be the constant speed at which the ring expands. Express your answers to the following questions in terms of r, v, a, b, R, B = B, and T as needed. Note that in this problem R is a resistance, not a radius. a) Give an expression for the induced current I in the ring. Draw the direction of the induced current on the figure above. You may ignore any magnetic field generated by the induced current. The current flows clockwise in the band. d Φ d 2 r 2 r dr 1 dφ 2π rbv = B π = B π I = = dt dt dt R dt R b) What is the rate at which energy is dissipated (Joule heating) during the time interval 0 t T? πrBv 4π r B v I R= R= R R c) What is the direction and magnitude of the force per unit length that the external agents must apply to overcome the magnetic force per unit length on the conducting band due to the induced current?. 11
12 At any given point on the band, the Id s B ext force is radially inward, and therefore at that point the external agents must exert a force per unit length given by df agents ds = I B ext = ˆrIB = ˆrIB = ˆr 2πrB2 v R d) Based on your result for the force per unit length in part c), what power do the external agents provide during the time interval 0 t T? Is this the same as your answer to part b)? If yes, explain why; if no, explain why not. Be sure to give your reasoning. An external agent at a given point on the band exerting a force on that ds section of the band does work at a rate given by F v = ds ˆr 2πrB2 v v = 2πrB2 v 2 ds. R R The power from all the agents is found by integrating the above over the circumference, giving 4π 2 r 2 B 2 v 2 / R, the same as above. They are the same because of conservation of energy. 12
Eðlisfræði 2, vor 2007
[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 28. Sources of Magnetic Field Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the deadline
More informationQ28.1 A positive point charge is moving to the right. The magnetic field that the point charge produces at point P (see diagram below) P
Q28.1 A positive point charge is moving to the right. The magnetic field that the point charge produces at point P (see diagram below) P r + v r A. points in the same direction as v. B. points from point
More informationPhysics 2212 GH Quiz #4 Solutions Spring 2015
Physics 1 GH Quiz #4 Solutions Spring 15 Fundamental Charge e = 1.6 1 19 C Mass of an Electron m e = 9.19 1 31 kg Coulomb constant K = 8.988 1 9 N m /C Vacuum Permittivity ϵ = 8.854 1 1 C /N m Earth s
More informationHomework #11 20311721 Physics 2 for Students of Mechanical Engineering
Homework #11 20311721 Physics 2 for Students of Mechanical Engineering 2. A circular coil has a 10.3 cm radius and consists of 34 closely wound turns of wire. An externally produced magnetic field of
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. 8.02 Spring 2013 Conflict Exam Two Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 802 Spring 2013 Conflict Exam Two Solutions Problem 1 (25 points): answers without work shown will not be given any credit A uniformly charged
More informationPhys222 Winter 2012 Quiz 4 Chapters 2931. Name
Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region
More informationPhysics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings
1 of 11 9/7/2012 1:06 PM Logged in as Julie Alexander, Instructor Help Log Out Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings Course Home Assignments Roster Gradebook Item Library
More informationPhysics 126 Practice Exam #3 Professor Siegel
Physics 126 Practice Exam #3 Professor Siegel Name: Lab Day: 1. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true? A) The magnetic force
More information1. A wire carries 15 A. You form the wire into a singleturn circular loop with magnetic field 80 µ T at the loop center. What is the loop radius?
CHAPTER 3 SOURCES O THE MAGNETC ELD 1. A wire carries 15 A. You form the wire into a singleturn circular loop with magnetic field 8 µ T at the loop center. What is the loop radius? Equation 33, with
More informationFall 12 PHY 122 Homework Solutions #8
Fall 12 PHY 122 Homework Solutions #8 Chapter 27 Problem 22 An electron moves with velocity v= (7.0i  6.0j)10 4 m/s in a magnetic field B= (0.80i + 0.60j)T. Determine the magnitude and direction of the
More informationEdmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).
INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes
More informationFaraday s Law of Induction
Chapter 10 Faraday s Law of Induction 10.1 Faraday s Law of Induction...1010.1.1 Magnetic Flux...103 10.1. Lenz s Law...105 10. Motional EMF...107 10.3 Induced Electric Field...1010 10.4 Generators...101
More informationCET Moving Charges & Magnetism
CET 2014 Moving Charges & Magnetism 1. When a charged particle moves perpendicular to the direction of uniform magnetic field its a) energy changes. b) momentum changes. c) both energy and momentum
More informationRUPHYS ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman
Signed in as Jolie Cizewski, Instructor Help Sign Out RUPHYS2272014 ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman Course Home Assignments Roster
More informationReview Questions PHYS 2426 Exam 2
Review Questions PHYS 2426 Exam 2 1. If 4.7 x 10 16 electrons pass a particular point in a wire every second, what is the current in the wire? A) 4.7 ma B) 7.5 A C) 2.9 A D) 7.5 ma E) 0.29 A Ans: D 2.
More informationMagnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.
Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.
More informationChapter 4. Electrostatic Fields in Matter
Chapter 4. Electrostatic Fields in Matter 4.1. Polarization A neutral atom, placed in an external electric field, will experience no net force. However, even though the atom as a whole is neutral, the
More informationVIII. Magnetic Fields  Worked Examples
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.0 Spring 003 VIII. Magnetic Fields  Worked Examples Example : Rolling rod A rod with a mass m and a radius R is mounted on two parallel rails
More informationPhysics 1653 Exam 3  Review Questions
Physics 1653 Exam 3  Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but
More informationLast Name: First Name: Physics 102 Spring 2006: Exam #2 MultipleChoice Questions 1. A charged particle, q, is moving with speed v perpendicular to a uniform magnetic field. A second identical charged
More informationSolution Derivations for Capa #11
Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5.0 V, = 155 Ω, L = 8.400 10 2 H. In the diagram above, what is the voltage across the
More informationPhys102 Lecture 18/19 Ampere's Law
Phys102 Lecture 18/19 Ampere's Law Key Points Ampère s Law Magnetic Field Due to a Straight Wire B Magnetic Field of a Solenoid and a Toroid References SFU Ed: 281,2,3,4,5. 6 th Ed: 205,6,7. Ampère s
More informationLecture 22. Inductance. Magnetic Field Energy. Outline:
Lecture 22. Inductance. Magnetic Field Energy. Outline: Selfinduction and selfinductance. Inductance of a solenoid. The energy of a magnetic field. Alternative definition of inductance. Mutual Inductance.
More informationExercises on Voltage, Capacitance and Circuits. A d = (8.85 10 12 ) π(0.05)2 = 6.95 10 11 F
Exercises on Voltage, Capacitance and Circuits Exercise 1.1 Instead of buying a capacitor, you decide to make one. Your capacitor consists of two circular metal plates, each with a radius of 5 cm. The
More informationPH 212 07312015 Physics 212 Exam3 Solution NAME: Write down your name also on the back of the package of sheets you turn in.
PH 1 73115 Physics 1 Exam3 Solution NAME: Write down your name also on the back of the package of sheets you turn in. SIGNATURE and ID: Return this hard copy exam together with your other answer sheets.
More informationMultiple Choice Questions for Physics 1 BA113 Chapter 23 Electric Fields
Multiple Choice Questions for Physics 1 BA113 Chapter 23 Electric Fields 63 When a positive charge q is placed in the field created by two other charges Q 1 and Q 2, each a distance r away from q, the
More informationChapter 22: Electric Flux and Gauss s Law
22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we
More informationProblem Solving 5: Magnetic Force, Torque, and Magnetic Moments
MASSACHUSETTS INSTITUTE OF TECHNOLOY Department of Physics Problem Solving 5: Magnetic Force, Torque, and Magnetic Moments OBJECTIVES 1. To start with the magnetic force on a moving charge q and derive
More informationModule 22: Inductance and Magnetic Field Energy
Module 22: Inductance and Magnetic Field Energy 1 Module 22: Outline Self Inductance Energy in Inductors Circuits with Inductors: RL Circuit 2 Faraday s Law of Induction dφ = B dt Changing magnetic flux
More informationChapter 14 Magnets and
Chapter 14 Magnets and Electromagnetism How do magnets work? What is the Earth s magnetic field? Is the magnetic force similar to the electrostatic force? Magnets and the Magnetic Force! We are generally
More informationHW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.
HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 22.P.053 The figure below shows a portion of an infinitely
More informationElectromagnetism Laws and Equations
Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E and Dfields............................................. Electrostatic Force............................................2
More informationPhysics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6. Instructions: 1. In the formula F = qvxb:
Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6 Signature Name (Print): 4 Digit ID: Section: Instructions: Answer all questions 24 multiple choice questions. You may need to do some calculation.
More informationPHY2049 Exam #2 Solutions Fall 2012
PHY2049 Exam #2 Solutions Fall 2012 1. The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial segments. The circuits
More information5.Magnetic Fields due to Currents( with Answers)
5.Magnetic Fields due to Currents( with Answers) 1. Suitable units for µ. Ans: TmA 1 ( Recall magnetic field inside a solenoid is B= µ ni. B is in tesla, n in number of turn per metre, I is current in
More information1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D
Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be
More informationExam 2 Solutions. PHY2054 Spring Prof. P. Kumar Prof. P. Avery March 5, 2008
Prof. P. Kumar Prof. P. Avery March 5, 008 Exam Solutions 1. Two cylindrical resistors are made of the same material and have the same resistance. The resistors, R 1 and R, have different radii, r 1 and
More informationForce on a square loop of current in a uniform Bfield.
Force on a square loop of current in a uniform Bfield. F top = 0 θ = 0; sinθ = 0; so F B = 0 F bottom = 0 F left = I a B (out of page) F right = I a B (into page) Assume loop is on a frictionless axis
More informationQuestion Details C14: Magnetic Field Direction Abbott [ ]
Phys 1114: Assignment 9 Abbott (5420633) Due: Mon Apr 7 2014 11:59 PM CDT Question 1 2 3 4 5 6 7 8 9 10 11 1. Question Details C14: Magnetic Field Direction Abbott [2861537] a) A wire is oriented horizontally
More informationElectromagnetic Induction
Electromagnetic Induction Lecture 29: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Mutual Inductance In the last lecture, we enunciated the Faraday s law according to
More informationExercises on the Magnetic Interaction
Exercises on the Magnetic Interaction Exercise 1.1 Consider two infinitely long conducting wires that are parallel to each other and lie in the xz plane. The wires are parallel to the zaxis, and are
More informationChapter 33. The Magnetic Field
Chapter 33. The Magnetic Field Digital information is stored on a hard disk as microscopic patches of magnetism. Just what is magnetism? How are magnetic fields created? What are their properties? These
More informationExam 1 Practice Problems Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8 Spring 13 Exam 1 Practice Problems Solutions Part I: Short Questions and Concept Questions Problem 1: Spark Plug Pictured at right is a typical
More informationChapter 27 Magnetic Field and Magnetic Forces
Chapter 27 Magnetic Field and Magnetic Forces  Magnetism  Magnetic Field  Magnetic Field Lines and Magnetic Flux  Motion of Charged Particles in a Magnetic Field  Applications of Motion of Charged
More informationForce on Moving Charges in a Magnetic Field
[ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after
More informationInductance. Motors. Generators
Inductance Motors Generators Selfinductance Selfinductance occurs when the changing flux through a circuit arises from the circuit itself. As the current increases, the magnetic flux through a loop due
More informationPhysics 25 Exam 3 November 3, 2009
1. A long, straight wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what would be the the magnitude of the magnetic field at a distance d/3 from the wire,
More informationPHY114 S11 Term Exam 3
PHY4 S Term Exam S. G. Rajeev Mar 2 20 2:0 pm to :45 pm PLEASE write your workshop number and your workshop leader s name at the top of your book, so that you can collect your graded exams at the workshop.
More informationProfs. A. Petkova, A. Rinzler, S. Hershfield. Exam 2 Solution
PHY2049 Fall 2009 Profs. A. Petkova, A. Rinzler, S. Hershfield Exam 2 Solution 1. Three capacitor networks labeled A, B & C are shown in the figure with the individual capacitor values labeled (all units
More informationConceptual: 1, 3, 5, 6, 8, 16, 18, 19. Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65. Conceptual Questions
Conceptual: 1, 3, 5, 6, 8, 16, 18, 19 Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65 Conceptual Questions 1. The magnetic field cannot be described as the magnetic force per unit charge
More informationMAGNETISM MAGNETISM. Principles of Imaging Science II (120)
Principles of Imaging Science II (120) Magnetism & Electromagnetism MAGNETISM Magnetism is a property in nature that is present when charged particles are in motion. Any charged particle in motion creates
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Print ] Eðlisfræði 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has
More informationCHAPTER 24 GAUSS S LAW
CHAPTER 4 GAUSS S LAW 4. The net charge shown in Fig. 440 is Q. Identify each of the charges A, B, C shown. A B C FIGURE 440 4. From the direction of the lines of force (away from positive and toward
More informationMagnetic fields of charged particles in motion
C H A P T E R 8 Magnetic fields of charged particles in motion CONCEPTS 8.1 Source of the magnetic field 8. Current loops and spin magnetism 8.3 Magnetic moment and torque 8.4 Ampèrian paths QUANTTATVE
More informationInduced voltages and Inductance Faraday s Law
Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic
More informationChapter 10. Faraday s Law of Induction
10 10 100 Chapter 10 Faraday s Law of Induction 10.1 Faraday s Law of Induction... 103 10.1.1 Magnetic Flux... 105 10.2 Motional EMF... 105 10.3 Faraday s Law (see also Faraday s Law Simulation in
More informationPhysics 104 Exam 2 Name
1. An electron moves with a velocity of 7.0 x 10 6 m/s due west in a uniform magnetic field of magnitude 4.0 T at an angle of 30 ast of orth. At the same point an electric field of magnitude 9.0 x 10 6
More informationChapter 20. Magnetic Induction Changing Magnetic Fields yield Changing Electric Fields
Chapter 20 Magnetic Induction Changing Magnetic Fields yield Changing Electric Fields Introduction The motion of a magnet can induce current in practical ways. If a credit card has a magnet strip on its
More informationInductance and Magnetic Energy
Chapter 11 Inductance and Magnetic Energy 11.1 Mutual Inductance... 113 Example 11.1 Mutual Inductance of Two Concentric Coplanar Loops... 115 11. SelfInductance... 115 Example 11. SelfInductance
More information104 Practice Exam 23/21/02
104 Practice Exam 23/21/02 1. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A nonzero
More informationDirection of Induced Current
Direction of Induced Current Bar magnet moves through coil Current induced in coil A S N v Reverse pole Induced current changes sign B N S v v Coil moves past fixed bar magnet Current induced in coil as
More informationExam 2 Practice Problems Part 1 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Exam Practice Problems Part 1 Solutions Problem 1 Electric Field and Charge Distributions from Electric Potential An electric potential V ( z
More informationClicker Question. A) Orientation A B) Orientation B
The circuit shown is constructed on a horizontal table and a compass is placed on top of the circuit as shown. Which way should the battery be placed in the circuit so when the switch is closed, the compass
More informationChapter 19 Magnetic Forces and Fields
Chapter 19 Magnetic Forces and Fields Student: 3. The magnetism of the Earth acts approximately as if it originates from a huge bar magnet within the Earth. Which of the following statements are true?
More informationThe purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.
260 171 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this
More informationPhysics 212 Lecture 15
Your Comments Prof, before you get too disappointed by the number of people who, "didn't think about this," understand that don't find value in completing the prelecture prelecture. t's much more useful
More informationPhysics 2220 Module 09 Homework
Physics 2220 Module 09 Homework 01. A potential difference of 0.050 V is developed across the 10cmlong wire of the figure as it moves though a magnetic field perpendicular to the page. What are the strength
More informationQuiz: Work and Energy
Quiz: Work and Energy A charged particle enters a uniform magnetic field. What happens to the kinetic energy of the particle? (1) it increases (2) it decreases (3) it stays the same (4) it changes with
More informationNAME. and 2I o. (1) Two long wires carry magnetic fields I o. , where I o
(1) Two long wires carry magnetic fields I o and 2I o, where I o is a constant. The two wires cross at the origin (but without making any electrical connection), and lie in the xy plane. (a) Find the
More informationMFF 3a: Charged Particle and a Straight CurrentCarrying Wire... 2
MFF 3a: Charged Particle and a Straight CurrentCarrying Wire... 2 MFF3a RT1: Charged Particle and a Straight CurrentCarrying Wire... 3 MFF3a RT2: Charged Particle and a Straight CurrentCarrying Wire...
More informationChapter 31: Induction and Inductance
Chapter 31: Induction and Inductance In Ch 30 we learned the following about magnetic fields: a) A magnetic field can exert a force on a current carrying wire b) If the wire is a closed loop then the magnetic
More informationExperiment 7: Forces and Torques on Magnetic Dipoles
MASSACHUSETTS INSTITUTE OF TECHNOLOY Department of Physics 8. Spring 5 OBJECTIVES Experiment 7: Forces and Torques on Magnetic Dipoles 1. To measure the magnetic fields due to a pair of currentcarrying
More informationPHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator.
PHYS 222 Spring 2012 Final Exam Closed books, notes, etc. No electronic device except a calculator. NAME: (all questions with equal weight) 1. If the distance between two point charges is tripled, the
More informationThe Electric Field. Electric Charge, Electric Field and a Goofy Analogy
. The Electric Field Concepts and Principles Electric Charge, Electric Field and a Goofy Analogy We all know that electrons and protons have electric charge. But what is electric charge and what does it
More information1. The diagram below represents magnetic lines of force within a region of space.
1. The diagram below represents magnetic lines of force within a region of space. 4. In which diagram below is the magnetic flux density at point P greatest? (1) (3) (2) (4) The magnetic field is strongest
More informationIMPORTANT NOTE ABOUT WEBASSIGN:
Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationLecture 14. Magnetic Forces on Currents.
Lecture 14. Magnetic Forces on Currents. Outline: Hall Effect. Magnetic Force on a Wire Segment. Torque on a CurrentCarrying Loop. Lecture 13: Magnetic Forces on Moving Charges  we considered individual
More information* Biot Savart s Law Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B. PPT No.
* Biot Savart s Law Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B PPT No. 17 Biot Savart s Law A straight infinitely long wire is carrying
More informationMagnetic Fields. I. Magnetic Field and Magnetic Field Lines
Magnetic Fields I. Magnetic Field and Magnetic Field Lines A. The concept of the magnetic field can be developed in a manner similar to the way we developed the electric field. The magnitude of the magnetic
More informationStress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t
Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a loadcarrying
More informationUniversity of California, Berkeley Physics H7B Spring 1999 (Strovink) SOLUTION TO PROBLEM SET 10 Solutions by P. Pebler
University of California, Berkeley Physics H7B Spring 1999 (Strovink) SOLUTION TO PROBLEM SET 10 Solutions by P Pebler 1 Purcell 66 A round wire of radius r o carries a current I distributed uniformly
More information11. Rotation Translational Motion: Rotational Motion:
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationName: Date: Regents Physics Mr. Morgante UNIT 4B Magnetism
Name: Regents Physics Date: Mr. Morgante UNIT 4B Magnetism Magnetism Magnetic Force exists b/w charges in motion. Similar to electric fields, an X stands for a magnetic field line going into the page,
More informationExperimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION ( )
a. Using Faraday s law: Experimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION The overall sign will not be graded. For the current, we use the extensive hints in the
More informationPhysics 112 Homework 5 (solutions) (2004 Fall) Solutions to Homework Questions 5
Solutions to Homework Questions 5 Chapt19, Problem2: (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in Figure P19.2, as shown. (b) Repeat
More informationMagnetic Field and Magnetic Forces
Chapter 27 Magnetic Field and Magnetic Forces PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 27 Magnets
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationChapter 30 Inductance
Chapter 30 Inductance In this chapter we investigate the properties of an inductor in a circuit. There are two kinds of inductance mutual inductance and selfinductance. An inductor is formed by taken
More informationMagnetic electromechanical machines
Magnetic electromechanical machines Lorentz Force A magnetic field exerts force on a moving charge. The Lorentz equation: f = q(e + v B) f: force exerted on charge q E: electric field strength v: velocity
More informationPhysics 9 Fall 2009 Homework 7  Solutions
Physics 9 Fall 009 Homework 7  s 1. Chapter 33  Exercise 10. At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your answer
More informationObjectives. Capacitors 262 CHAPTER 5 ENERGY
Objectives Describe a capacitor. Explain how a capacitor stores energy. Define capacitance. Calculate the electrical energy stored in a capacitor. Describe an inductor. Explain how an inductor stores energy.
More informationPractice final for Basic Physics spring 2005 answers on the last page Name: Date:
Practice final for Basic Physics spring 2005 answers on the last page Name: Date: 1. A 12 ohm resistor and a 24 ohm resistor are connected in series in a circuit with a 6.0 volt battery. Assuming negligible
More informationQuestion Bank. 1. Electromagnetism 2. Magnetic Effects of an Electric Current 3. Electromagnetic Induction
1. Electromagnetism 2. Magnetic Effects of an Electric Current 3. Electromagnetic Induction 1. Diagram below shows a freely suspended magnetic needle. A copper wire is held parallel to the axis of magnetic
More informationChapter 22: The Electric Field. Read Chapter 22 Do Ch. 22 Questions 3, 5, 7, 9 Do Ch. 22 Problems 5, 19, 24
Chapter : The Electric Field Read Chapter Do Ch. Questions 3, 5, 7, 9 Do Ch. Problems 5, 19, 4 The Electric Field Replaces actionatadistance Instead of Q 1 exerting a force directly on Q at a distance,
More informationRUPHYS2272015 ( RUPHY227F2015 ) My Courses Course Settings University Physics with Modern Physics, 14e Young/Freedman
Signed in as Jolie Cizewski, Instructor Help Sign Out RUPHYS2272015 ( RUPHY227F2015 ) My Courses Course Settings University Physics with Modern Physics, 14e Young/Freedman Course Home Assignments Roster
More informationPhysics 6C, Summer 2006 Homework 1 Solutions F 4
Physics 6C, Summer 006 Homework 1 Solutions All problems are from the nd edition of Walker. Numerical values are different for each student. Chapter Conceptual Questions 18. Consider the four wires shown
More informationGauss s Law for Gravity
Gauss s Law for Gravity D.G. impson, Ph.D. Department of Physical ciences and Engineering Prince George s Community College December 6, 2006 Newton s Law of Gravity Newton s law of gravity gives the force
More informationChapter 4. Magnetic Materials and Circuits
Chapter 4 Magnetic Materials and Circuits Objectives List six characteristics of magnetic field. Understand the righthand rule for current and magnetic fluxes. Define magnetic flux, flux density, magnetomotive
More informationF = 0. x ψ = y + z (1) y ψ = x + z (2) z ψ = x + y (3)
MATH 255 FINAL NAME: Instructions: You must include all the steps in your derivations/answers. Reduce answers as much as possible, but use exact arithmetic. Write neatly, please, and show all steps. Scientists
More information