Lecture 22. Inductance. Magnetic Field Energy. Outline:


 Delphia Jewel Singleton
 1 years ago
 Views:
Transcription
1 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. 1
2  CH2 exam average ~54 %.  To the right are VERY tentative correlations between percentage scores and letter grades in Physics 227. The instructors reserve the right to adjust these boundaries (both up and down) before final grades are assigned at the end of the semester. A B+ < B < C+ < C < D < < F 2
3 Maxwell s Equations Gauss s Law: charges are sources of electric field (and a nonzero net electric field flux through a closed surface); field lines begin and end on charges. ssss E da = Q eeee ε 0 No magnetic monopoles; magnetic field lines form closed loops. ssss B da = 0 Faraday s Law of electromagnetic induction; a timedependent Φ B generates E. looo E dl = d B da suuu E = dφ B Generalized Ampere s Law; B is produced by both currents and timedependent Φ E. looo E B dl = μ 0 J + ε 0 suuu da The force on a (moving) charge. F = q E + v B 3
4 Iclicker Question loop 1 loop 2 Two identical concentric loops are arranged as shown in the Figure. One loop has a steady current flowing through it (provided by a power supply). When the power is turned off, in what direction does the induced current flow in loop 2? A. It flows clockwise. B. It flows counterclockwise. C. There is no induced current. D. Something else happens. E. The answer depends on what direction the current was flowing in loop 1. 4
5 Iclicker Question loop 1 loop 2 Two identical concentric loops are arranged as shown in the Figure. One loop has a steady current flowing through it (provided by the power supply). When the power is turned off, in what direction does the induced current flow in loop 2? A. It flows clockwise. B. It flows counterclockwise. C. There is no induced current. D. Something else happens. E. The answer depends on what direction the current was flowing in loop 1. 5
6 Iclicker Question loop 1 loop 2 Two identical concentric loops are arranged as shown in the Figure. One loop has a steady current flowing through it (provided by the power supply). When the power is turned off, will the two loops briefly attract or repel each other? A. They will attract each other. B. They will repel each other. C. There is no induced current. D. They will neither repel nor attract each other. E. The answer depends on the direction of current in loop 1. 6
7 Iclicker Question loop 1 loop 2 Two identical concentric loops are arranged as shown in the Figure. One loop has a steady current flowing through it (provided by the power supply). When the power is turned off, will the two loops briefly attract or repel each other? A. They will attract each other. B. They will repel each other. C. There is no induced current. D. They will neither repel nor attract each other. E. The answer depends on the direction of current in loop 1. 7
8 Induced E.M.F. and its consequences 1. FFFFFFF: E = dφ B 2. I t eeeeeeee B t 3. I t B t 8
9 (Self) Inductance Variable battery I t FFFFFFF: E = dφ B B t The flux depends on the current, so a wire loop with a changing current induces an aitional e.m.f. in itself that opposes the changes in the current and, thus, in the magnetic flux (sometimes called the back e.m.f.). The back e.m.f. : E = dφ B = L L the coefficient of proportionality between Φ and I, purely geometrical quantity. Inductance: (or selfinductance) L Φ I Units: T m 2 /A = Henry (H) The selfinductance L is always positive. This definition applies when there is a single current path (see below for an inductance of a system of distributed currents J r ). Inductance as a circuit element: 9
10 Inductance of a Long Solenoid Long solenoid of radius r and length l with the total number of turns N: L Φ B I l The magnetic flux generated by current I: Φ B = Bπr 2 N = B = μ 0 N l I = μ 0N 2 I l πr 2 = μ 0 n 2 I l πr 2 L = Φ B I = μ 0N 2 l πr 2 = μ 0 n 2 l πr 2 (n the number of turns per unit length) Note that  the inductance scales with the solenoid volume l πr 2 ;  the inductance scales as N 2 : B is proportional to N l and the net flux N. Let s plug some numbers: l =0.1m, N=100, r=0.01m L = μ 0 n 2 l πr 2 = 4π π μμ How significant is the induced e.m.f.? For ~104 A/s (let s say, I~ 1 ma in 0.1 µs) E = L = H A s = 0.4V 10
11 Iclicker Question A current i flows through an inductor L in the direction from point b toward point a. There is zero resistance in the wires of the inductor. If the current is decreasing, A. the potential is greater at point a than at point b. B. the potential is less at point a than at point b. C. the answer depends on the magnitude of di/dt compared to the magnitude of i. D. The answer depends on the value of the inductance L. E. both C. and D. are correct. 11
12 Iclicker Question A current i flows through an inductor L in the direction from point b toward point a. There is zero resistance in the wires of the inductor. If the current is decreasing, A. the potential is greater at point a than at point b. B. the potential is less at point a than at point b. C. the answer depends on the magnitude of di/dt compared to the magnitude of i. D. The answer depends on the value of the inductance L. E. both C. and D. are correct. 12
13 Inductance vs. Resistance Inductor affects the current flow only if there is a change in current (di/dt 0). The sign of di/dt determines the sign of the induced e.m.f. The higher the frequency of current variations, the larger the induced e.m.f. 13
14 Energy of Magnetic Field To increase a current in a solenoid, we have to do some work: we work against the back e.m.f. V i t Let s ramp up the current from 0 to the final value I (i t is the instantaneous current value): V t = L t P t = V t i t = L t i t i t The net work to ramp up the current from 0 to I : = P t f U = P t i P(power)  the rate at which energy is being delivered to the inductor from external sources. I = LL 0 = 1 2 LI2 U = 1 2 LI2 This energy is stored in the magnetic field created by the current. L = μ 0 n 2 l πr 2 = μ 0 n 2 vvvvvv U B = 1 2 μ 0n 2 vvvvvv I 2 = B = μ 0 nn = B2 2μ 0 vvvvvv = u B vvvvvv The energy density in a magnetic field: u B = B2 2μ 0 (compare with u E = This is a general result (not solenoidspecific). ε 0E2 2 ) 14
15 Quench of a Superconducting Solenoid MRI scanner: the magnetic field up to 3T within a volume ~ 1 m 3. The magnetic field energy: U = vvvvvv u B = 1m 3 3T 2 2 4π 10 7 WW A m 4MM The capacity of the LHe dewar: ~2,000 liters. The heat of vaporization of liquid helium: 3 kj/liter. Thus, ~ 1000 liters will be evaporated during the quench. Magnet quench: 15
16 Another (More General) Definition of Inductance Alternative definition of inductance: 1 2 LI2 = B2 2μ 0 dτ all sssss L 2U B I 2 Advantage: it works for a distributed current flow (when it s unclear which loop we need to consider for the flux calculation). 16
17 Example: inductance per unit length for a coaxial cable I I b a Uniform current density in the central conductor of radius a: b U B = 1 2μ 0 B r 0 2 dτ B r = μ 0 I, a < r < b 2ππ μ 0 Ir, r < a 2πa2 at home L = 2U B I 2 Straight Wires: Do They Have Inductance? Using L = 2U B /I 2 : U B = 1 2μ 0 a b μ 0I 2ππ 2 Using L = Φ/I: ~l B μ 0I 2ππ l dτ b = 1 2μ 0 a μ 0I 2ππ l Φ l μ 0I 2ππ a 2 l 2ππππ = μ 0I 2π l ll l a (b~l ) μ 0I 2 4π l ll l a L H μ 0 2π l ll l a l m ll l a l = 1cc L 10 9 H L H μ 0 2π l ll l a 17
18 Inductance vs. Capacitance L = Φ B I = 2U B I 2 C = Q V = 2U E V 2 U B = 1 2 LI2 = 1 2 Φ B 2 L U B = B2 2μ 0 vvvvvv = u B vvvvvv Q 2 U E = 1 2 CV2 = 1 2 C U E = ε 0E 2 2 vvvvvv = u E vvvvvv 18
19 Mutual Inductance Let s consider two wire loops at rest. A timedependent current in loop 1 produces a timedependent magnetic field B 1. The magnetic flux is linked to loop 1 as well as loop 2. Faraday s law: the time dependent flux of B 1 induces e.m.f. in both loops. B 1 I 1 loop 2 loop 1 Primitive transformer The e.m.f. in loop 2 due to the timedependent I 1 in loop 1: E 2 = dφ 1 2 Φ 1 2 = M 1 2 I 1 The flux of B 1 in loop 2 is proportional to the current I 1 in loop 1. The coefficient of proportionality M 1 2 (the socalled mutual inductance) is, similar to L, a purely geometrical quantity; its calculation requires, in general, complicated integration. Also, it s possible to show that M 1 2 = M 2 1 = M so there is just one mutual inductance M. M can be either positive or negative, depending on the choices made for the senses of transversal about loops 1 and 2. Units of the (mutual) inductance Henry (H). E 2 = M I 1 M = Φ 1 2 I 1 19
20 Calculation of Mutual Inductance Calculate M for a pair of coaxial solenoids (r 1 = r 2 = r, l 1 = l 2 = l, n 1 and n 2  the densities of turns). l B 1 = μ 0 n 1 I 1 Φ = B 1 πr 2 = μ 0 n 1 I 1 πr 2 M 1 2 = M 2 1 = M L = μ 0 n 2 l πr 2 = μ 0N 2 πr 2 Experiment with two coaxial coils. l the flux per one turn M = N 2Φ = N I 2 μ 0 n 1 πr 2 = μ 0N 1 N 2 πr 2 1 l M = L 1 L 2 The induced e.m.f. in the secondary coil is much greater if we use a ferromagnetic core: for a given current in the first coil the magnetic flux (and, thus the mutual inductance) will be ~K m times greater. E 2 = M di 1 = K m M di 1 nocore mutual inductance 20
21 Next time: Lecture 23. RL and LC circuits
22 Appendix I: Inductance of a Circular Wire Loop 2a b Example: estimate the inductance of a circular wire loop with the radius of the loop, b, being much greater than the wire radius a. The field dies off rapidly (~1/r) with distance from the wire, so it won t be a big mistake to approximate the loop as a straight wire of length 2πb, and integrate the flux through a strip of the width b: b B μ 0I 2ππ 2πb Note that we cannot assume that the wire radius is zero: b Φ 2ππ μ 0I 2ππ = μ 0 bi ll b a a L b = 1m, a = 10 3 m 4π 10 7 L = Φ I μ 0b ll b a WW A m 1m ll103 10μμ b Φ~ μ 0I 2ππ "0" ~ll b "0"  diverges! What to do: introduce some reasonably small nonzero radius. 22
Induced 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 informationPhysics 2102 Lecture 19. Physics 2102
Physics 2102 Jonathan Dowling Physics 2102 Lecture 19 Ch 30: Inductors and RL Circuits Nikolai Tesla What are we going to learn? A road map Electric charge Electric force on other electric charges Electric
More informationSlide 1 / 26. Inductance. 2011 by Bryan Pflueger
Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one
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 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 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 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 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 informationFall 12 PHY 122 Homework Solutions #10
Fall 12 PHY 122 Homework Solutions #10 HW10: Ch.30 Q5, 8, 15,17, 19 P 1, 3, 9, 18, 34, 36, 42, 51, 66 Chapter 30 Question 5 If you are given a fixed length of wire, how would you shape it to obtain the
More information12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its selfinductance?
12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its selfinductance? From Equation 325, L = E=(dI =dt) = 40 V=(100 A/s) = 0.4 H. 15. A cardboard
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 informationChapter 30 Inductance
Chapter 30 Inductance  Mutual Inductance  SelfInductance and Inductors  MagneticField Energy  The R Circuit  The C Circuit  The RC Series Circuit . Mutual Inductance  A changing current in
More informationProblem 1 (25 points)
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
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 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 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 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 informationChapter 11. Inductors ISU EE. C.Y. Lee
Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive
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 informationEE301 Lesson 14 Reading: 10.110.4, 10.1110.12, 11.111.4 and 11.1111.13
CAPACITORS AND INDUCTORS Learning Objectives EE301 Lesson 14 a. Define capacitance and state its symbol and unit of measurement. b. Predict the capacitance of a parallel plate capacitor. c. Analyze how
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 informationPhysics 9 Fall 2009 Homework 8  Solutions
1. Chapter 34  Exercise 9. Physics 9 Fall 2009 Homework 8  s The current in the solenoid in the figure is increasing. The solenoid is surrounded by a conducting loop. Is there a current in the loop?
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 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 information1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole.
Exam Name 1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole. 2) Which of the following statements is correct? A) Earth's north pole is magnetic north. B) The north
More informationMarch 20. Physics 272. Spring 2014 Prof. Philip von Doetinchem
Physics 272 March 20 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  129 Summary No magnetic
More informationLast time : energy storage elements capacitor.
Last time : energy storage elements capacitor. Charge on plates Energy stored in the form of electric field Passive sign convention Vlt Voltage drop across real capacitor can not change abruptly because
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 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 informationElectromagnetism Laws and Equations
Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E and Dfields............................................. Electrostatic Force............................................2
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 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 informationCircuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49
Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large
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 information"  angle between l and a R
Magnetostatic Fields According to Coulomb s law, any distribution of stationary charge produces a static electric field (electrostatic field). The analogous equation to Coulomb s law for electric fields
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 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 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 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 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 informationEðlisfræði 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 informationW03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören
W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018  Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and
More informationLecture 24. Inductance and Switching Power Supplies (how your solar charger voltage converter works)
Lecture 24 Inductance and Switching Power Supplies (how your solar charger voltage converter works) Copyright 2014 by Mark Horowitz 1 Roadmap: How Does This Work? 2 Processor Board 3 More Detailed Roadmap
More informationAP Physics C: Electricity and Magnetism: Syllabus 3
AP Physics C: Electricity and Magnetism: Syllabus 3 Scoring Components SC1 SC2 SC3 SC SC5 SC6 SC7 The course provides and provides instruction in electrostatics. The course provides and provides instruction
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 informationCourse Syllabus: AP Physics C Electricity and Magnetism
Course Syllabus: AP Physics C Electricity and Magnetism Course Description: AP Physics C is offered as a second year physics course to students who are planning to major in the physical sciences or in
More informationElectromagnetic Induction
Electromagnetic Induction "Concepts without factual content are empty; sense data without concepts are blind... The understanding cannot see. The senses cannot think. By their union only can knowledge
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 informationCoupling Magnetic Signals to a SQUID Amplifier
SQUID Application Note 1050 Coupling Magnetic Signals to a SQUID Amplifier Matching the effective inductances of the Pickup Coil and the Input Coil to detect and couple magnetic flux maximizes the sensitivity
More informationDEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING
SESSION WEEK COURSE: Physics II DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING DESCRIPTION GROUPS (mark ) Indicate YES/NO If the session needs 2
More informationEEE1001/PHY1002. Magnetic Circuits. The circuit is of length l=2πr. B andφ circulate
1 Magnetic Circuits Just as we view electric circuits as related to the flow of charge, we can also view magnetic flux flowing around a magnetic circuit. The sum of fluxes entering a point must sum to
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 informationLecture 13. Magnetic Field, Magnetic Forces on Moving Charges. Outline:
Lecture 13. Magnetic Field, Magnetic Forces on Moving Charges. Outline: Intro to Magnetostatics. Magnetic Field Flux, Absence of Magnetic Monopoles. Force on charges moving in magnetic field. 1 Intro to
More information2. A conductor of length 2m moves at 4m/s at 30 to a uniform magnetic field of 0.1T. Which one of the following gives the e.m.f. generated?
Extra Questions  2 1. A straight length of wire moves through a uniform magnetic field. The e.m.f. produced across the ends of the wire will be maximum if it moves: a) along the lines of magnetic flux
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 informationAP Physics CElectricity and Magnetism Syllabus
AP Physics CElectricity and Magnetism Syllabus Overview Students enrolled in AP Physics C have already completed a yearlong, accelerated physics course in their junior year. It is required that they
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 informationES250: Electrical Science. HW7: Energy Storage Elements
ES250: Electrical Science HW7: Energy Storage Elements Introduction This chapter introduces two more circuit elements, the capacitor and the inductor whose elements laws involve integration or differentiation;
More informationMutual inductance. Resources and methods for learning about these subjects (list a few here, in preparation for your research):
Mutual inductance This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationMutual Inductance and Transformers F3 3. r L = ω o
utual Inductance and Transformers F3 1 utual Inductance & Transformers If a current, i 1, flows in a coil or circuit then it produces a magnetic field. Some of the magnetic flux may link a second coil
More informationDiodes have an arrow showing the direction of the flow.
The Big Idea Modern circuitry depends on much more than just resistors and capacitors. The circuits in your computer, cell phone, Ipod depend on circuit elements called diodes, inductors, transistors,
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 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 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 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 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 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 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 informationChapter 27 Electromagnetic Induction
For us, who took in Faraday s ideas so to speak with our mother s milk, it is hard to appreciate their greatness and audacity. Albert Einstein 27.1 ntroduction Since a current in a wire produces a magnetic
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 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 informationExtra Questions  1. 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A
Extra Questions  1 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A 2. A current of 500mA flows in a resistance of 12Ω. What power is dissipated
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 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 informationAP Physics C: Electricity and Magnetism: Syllabus 2
AP Physics C: Electricity and Magnetism: Syllabus 2 Scoring Components SC1 SC2 SC SC SC5 SC6 SC7 The course provides and provides instruction in electrostatics. The course provides and provides instruction
More informationAP R Physics C Electricity and Magnetism Syllabus
AP R Physics C Electricity and Magnetism Syllabus 1 Prerequisites and Purposes of AP R C E & M AP R Physics C Electricity and Magnetism is the second course in a twocourse sequence. It is offered in the
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 informationApplication Note. So You Need to Measure Some Inductors?
So You Need to Measure Some nductors? Take a look at the 1910 nductance Analyzer. Although specifically designed for production testing of inductors and coils, in addition to measuring inductance (L),
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 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 information) 0.7 =1.58 10 2 N m.
Exam 2 Solutions Prof. Paul Avery Prof. Andrey Korytov Oct. 29, 2014 1. A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal sides, each with length L = 15 cm as
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 informationLinear DC Motors. 15.1 Magnetic Flux. 15.1.1 Permanent Bar Magnets
Linear DC Motors The purpose of this supplement is to present the basic material needed to understand the operation of simple DC motors. This is intended to be used as the reference material for the linear
More informationAP Physics C: Electricity and Magnetism 2011 Scoring Guidelines
AP Physics C: Electricity and Magnetism 11 Scoring Guidelines The College Board The College Board is a notforprofit membership association whose mission is to connect students to college success and
More informationOutline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... )
Outline Systems and Signals 214 / 244 & Energy Systems 244 / 344 Inductance, Leakage Inductance, Mutual Inductance & Transformers 1 Inductor revision Ideal Inductor NonIdeal Inductor Dr. P.J. Randewijk
More informationA wave lab inside a coaxial cable
INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S01430807(04)76273X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera
More informationCapacitors in Circuits
apacitors in ircuits apacitors store energy in the electric field E field created by the stored charge In circuit apacitor may be absorbing energy Thus causes circuit current to be reduced Effectively
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 informationPhysics 6C, Summer 2006 Homework 2 Solutions
Physics 6C, Summer 006 Homework Solutions All problems are from the nd edition of Walker. Numerical values are different for each student. Chapter 3 Problems. Figure 330 below shows a circuit containing
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 informationMagnetostatics (Free Space With Currents & Conductors)
Magnetostatics (Free Space With Currents & Conductors) Suggested Reading  Shen and Kong Ch. 13 Outline Review of Last Time: Gauss s Law Ampere s Law Applications of Ampere s Law Magnetostatic Boundary
More informationLenz's Law: A Relativistic Explanation
Lenz's Law: A Relativistic Explanation R. Sivron and N.R. Sivron (deceased) Physics Department, Baker University Abstract Einstein (and many since) stated that a primary purpose of his first paper on special
More informationElectrical Machines II. Week 1: Construction and theory of operation of single phase transformer
Electrical Machines II Week 1: Construction and theory of operation of single phase transformer Transformers Overview A transformer changes ac electric power at one frequency and voltage level to ac electric
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 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 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 informationThe March/April Morseman Problem
The Problem as stated was: The March/April Morseman Problem A toroidal transformer is used in directional coupler versions of an SWR bridge. The primary winding is the single wire running through the toroid,
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 informationChapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits. Copyright 2009 Pearson Education, Inc.
Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits 301 Mutual Inductance Mutual inductance: a changing current in one coil will induce a current in a second coil: Coil 1 produces a flux
More informationThe current that flows is determined by the potential difference across the conductor and the resistance of the conductor (Ohm s law): V = IR P = VI
PHYS1000 DC electric circuits 1 Electric circuits Electric current Charge can move freely in a conductor if an electric field is present; the moving charge is an electric current (SI unit is the ampere
More information