Problem 1 (25 points)


 Ella Hunt
 6 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationElectromagnetism Laws and Equations
Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E and Dfields............................................. Electrostatic Force............................................2
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationHow To Understand The Physics Of A Charge Charge
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 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 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 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 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 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 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 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 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 informationpotential in the centre of the sphere with respect to infinity.
Umeå Universitet, Fysik 1 Vitaly Bychkov Prov i fysik, Electricity and Waves, 20060927, kl 16.0022.00 Hjälpmedel: Students can use any book. Define the notations you are using properly. Present your
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
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 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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If the voltage at a point in space is zero, then the electric field must be A) zero. B) positive.
More informationA METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS
A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS Joseph J. Stupak Jr, Oersted Technology Tualatin, Oregon (reprinted from IMCSD 24th Annual Proceedings 1995) ABSTRACT The
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 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 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 informationMagnetic Circuits. Outline. Ampere s Law Revisited Review of Last Time: Magnetic Materials Magnetic Circuits Examples
Magnetic Circuits Outline Ampere s Law Revisited Review of Last Time: Magnetic Materials Magnetic Circuits Examples 1 Electric Fields Magnetic Fields S ɛ o E da = ρdv B V = Q enclosed S da =0 GAUSS GAUSS
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 informationAmpere's Law. Introduction. times the current enclosed in that loop: Ampere's Law states that the line integral of B and dl over a closed path is 0
1 Ampere's Law Purpose: To investigate Ampere's Law by measuring how magnetic field varies over a closed path; to examine how magnetic field depends upon current. Apparatus: Solenoid and path integral
More informationScott Hughes 7 April 2005. Massachusetts Institute of Technology Department of Physics 8.022 Spring 2005. Lecture 15: Mutual and Self Inductance.
Scott Hughes 7 April 2005 151 Using induction Massachusetts nstitute of Technology Department of Physics 8022 Spring 2005 Lecture 15: Mutual and Self nductance nduction is a fantastic way to create EMF;
More informationThe DC Motor. Physics 1051 Laboratory #5 The DC Motor
The DC Motor Physics 1051 Laboratory #5 The DC Motor Contents Part I: Objective Part II: Introduction Magnetic Force Right Hand Rule Force on a Loop Magnetic Dipole Moment Torque Part II: Predictions Force
More informationIf Σ is an oriented surface bounded by a curve C, then the orientation of Σ induces an orientation for C, based on the RightHandRule.
Oriented Surfaces and Flux Integrals Let be a surface that has a tangent plane at each of its nonboundary points. At such a point on the surface two unit normal vectors exist, and they have opposite directions.
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 informationExam 2 Practice Problems Part 2 Solutions
Problem 1: Short Questions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8. Exam Practice Problems Part Solutions (a) Can a constant magnetic field set into motion an electron, which is initially
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 informationChapter 19: Magnetic Forces and Fields
Chapter 19: Magnetic Forces and Fields Magnetic Fields Magnetic Force on a Point Charge Motion of a Charged Particle in a Magnetic Field Crossed E and B fields Magnetic Forces on Current Carrying Wires
More informationAP2 Magnetism. (c) Explain why the magnetic field does no work on the particle as it moves in its circular path.
A charged particle is projected from point P with velocity v at a right angle to a uniform magnetic field directed out of the plane of the page as shown. The particle moves along a circle of radius R.
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 12 Electricity and Magnetism Magnetism Magnetic fields and force Application of magnetic forces http://www.physics.wayne.edu/~apetrov/phy2140/ Chapter 19 1 Department
More informationQ27.1 When a charged particle moves near a bar magnet, the magnetic force on the particle at a certain point depends
Q27.1 When a charged particle moves near a bar magnet, the magnetic force on the particle at a certain point depends A. on the direction of the magnetic field at that point only. B. on the magnetic field
More informationChapter 28 Fluid Dynamics
Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example
More information6 J  vector electric current density (A/m2 )
Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J  vector electric current density (A/m2 ) M  vector magnetic current density (V/m 2 ) Some problems
More informationELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES
ELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES The purpose of this lab session is to experimentally investigate the relation between electric field lines of force and equipotential surfaces in two dimensions.
More informationChapter 30  Magnetic Fields and Torque. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 30  Magnetic Fields and Torque A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should
More informationExperiment 3: Magnetic Fields of a Bar Magnet and Helmholtz Coil
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2006 Experiment 3: Magnetic Fields of a Bar Magnet and Helmholtz Coil OBJECTIVES 1. To learn how to visualize magnetic field lines
More informationSteady Heat Conduction
Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long
More informationApril 1. Physics 272. Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html. Prof. Philip von Doetinchem philipvd@hawaii.
Physics 272 April 1 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272  Spring 14  von Doetinchem  164 Summary Gauss's
More informationExperiment 3: Magnetic Fields of a Bar Magnet and Helmholtz Coil
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2009 Experiment 3: Magnetic Fields of a Bar Magnet and Helmholtz Coil OBJECTIVES 1. To learn how to visualize magnetic field lines
More informationphysics 112N magnetic fields and forces
physics 112N magnetic fields and forces bar magnet & iron filings physics 112N 2 bar magnets physics 112N 3 the Earth s magnetic field physics 112N 4 electro magnetism! is there a connection between electricity
More informationPhysics 53. Kinematics 2. Our nature consists in movement; absolute rest is death. Pascal
Phsics 53 Kinematics 2 Our nature consists in movement; absolute rest is death. Pascal Velocit and Acceleration in 3D We have defined the velocit and acceleration of a particle as the first and second
More informationMagnetic Field of a Circular Coil Lab 12
HB 112607 Magnetic Field of a Circular Coil Lab 12 1 Magnetic Field of a Circular Coil Lab 12 Equipment coil apparatus, BK Precision 2120B oscilloscope, Fluke multimeter, Wavetek FG3C function generator,
More informationE X P E R I M E N T 8
E X P E R I M E N T 8 Torque, Equilibrium & Center of Gravity Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics, Exp 8:
More informationInductors & Inductance. Electronic Components
Electronic Components Induction In 1824, Oersted discovered that current passing though a coil created a magnetic field capable of shifting a compass needle. Seven years later, Faraday and Henry discovered
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationUnit 4 Practice Test: Rotational Motion
Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013
PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be
More informationǫ 0 = 8.85419 10 12 C 2 /N m 2,
Version 001 review unit chiu 58655 1 This printout should have 45 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The long negatively charged
More informationMagnetic Dipoles. Magnetic Field of Current Loop. B r. PHY2061 Enriched Physics 2 Lecture Notes
Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study aid and a supplement to
More informationChapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.
Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems
More informationPhysics 1A Lecture 10C
Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. Oprah Winfrey Static Equilibrium
More informationLesson 3 DIRECT AND ALTERNATING CURRENTS. Task. The skills and knowledge taught in this lesson are common to all missile repairer tasks.
Lesson 3 DIRECT AND ALTERNATING CURRENTS Task. The skills and knowledge taught in this lesson are common to all missile repairer tasks. Objectives. When you have completed this lesson, you should be able
More informationChapter 7. Magnetism and Electromagnetism ISU EE. C.Y. Lee
Chapter 7 Magnetism and Electromagnetism Objectives Explain the principles of the magnetic field Explain the principles of electromagnetism Describe the principle of operation for several types of electromagnetic
More informationPROBLEM SET. Practice Problems for Exam #1. Math 1352, Fall 2004. Oct. 1, 2004 ANSWERS
PROBLEM SET Practice Problems for Exam # Math 352, Fall 24 Oct., 24 ANSWERS i Problem. vlet R be the region bounded by the curves x = y 2 and y = x. A. Find the volume of the solid generated by revolving
More informationD Alembert s principle and applications
Chapter 1 D Alembert s principle and applications 1.1 D Alembert s principle The principle of virtual work states that the sum of the incremental virtual works done by all external forces F i acting in
More informationProblem 6.40 and 6.41 Kleppner and Kolenkow Notes by: Rishikesh Vaidya, Physics Group, BITSPilani
Problem 6.40 and 6.4 Kleppner and Kolenkow Notes by: Rishikesh Vaidya, Physics Group, BITSPilani 6.40 A wheel with fine teeth is attached to the end of a spring with constant k and unstretched length
More information