Faraday s Law and Inductance

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Faraday s Law and Inductance"

Transcription

1 Historical Overview Faraday s Law and Inductance So far studied electric fields due to stationary charges and magentic fields due to moving charges. Now study electric field due to a changing magnetic field. Faraday showed that an electric current can be induced in a circuit by a changing magnetic field. These studies lead to Faraday s law of induction. Faraday s law of induction A straight metal wire lies in a uniform magnetic field directed into the page. The wire contains free elctrons. Move the wire with a velocity v to the right. F = qv B implies that a magnetic force acts on the wire. Can use the right hand rule to show that the force on the electrons is downward, along the wire. The electrons move along the wire in response to this force: a current. Consider a loop of wire connected to a sensitive ammeter. Move a magnet toward the loop, the ammeter needle deflects in one direction. If the magnet is stationary, no current is detected. If the magnet is stationary and the coil is moved either away or toward it, a current is detected. An electric force is set up in the coil as long as relative motion occurs between the magnet and the coil. The current in the wire is called an induced current, produced by an induced electromotive force or emf. Faraday concluded that an electric current can be produced by a timevarying magnetic field. In the example above, what causes the time-varying magnetic field? Current cannot be produced by a steady magnetic field. Discuss Figure 23.3 To quantify this, define magnetic flux. 1

2 Consider an element of area da on an arbitrarily shaped open surface. If the magnetic field at the location of this element is B, the magnetic flux through the element is B.dA, where doverlinea is a vector perpendicular to the surface whose magnitude equals area da. Then the total magnetic flux through the surface is Φ B = B.A SI unit of magnetic flux is tesla-meter squared, where 1 weber or Wb = 1T.m 2. an emf is induced in a circuit when the magnetic flux through the surface bounded by the circuit changes with time. Faradays law of induction states that the emf induced in a circuit is equal to the time rate of change of magnetic flux through the circuit. ɛ = dφ B dt, where Φ B is the magnetic flux through the surface bounded by the circuit. If the circuit is a coil consisting of N identical and concentric loops and if the field lines pass through all loops, the induced emf is Why is cosθ needed here. ɛ = N dφ B ɛ = d dt (BAcosθ). Thus an emf can be induced in a circuit by changing the magnetic flux in several ways: Motional emf magnitude of B can vary with time the area A of the circuit can change with time the angle θ between B and the normal to the plane can change with time any combination of these changes Try QuickQuiz 23.1, go over example An emf is induced in a conductor moving through a magnetic field - motional emf. 2

3 Go over Figure The Alternating Current generator The alternating-current (AC) generator is a device in which energy is transferred in by work and out by electrical transmission: A coil of wire rotated in an external magnetic field by some external agent - this is the work input. For example, in a hydroelectric power plant, falling water directed against the blades of a turbine produces the rotary motion. As the loop rotates, the magnetic flux through it changes with time, inducing an emf and a current in a circuit connected to the coil. Suppose the coil has N turns of the same area A and suppose the coil rotates with a constant angular speed ω about an axis perpendicular to the magnetic field. If θ is the angle between the magnetic field and the direction perpendicular to the plane of the coil, the magnetic flux through the loop at any time t is given by: where θ = ωt. Φ B = BAcosθ = BAcosωt, Thus the induced emf in the coil is ɛ = N dφ B dt = NAB d dt (cosωt) = NABsinωt. Thus the emf varies sinusoidally with time - AC voltage. Lenz s Law Negative sign in Faraday s law. The polarity of the induced emf in a loop is such that it produces a current whose magentic field opposes the change in magnetic flux through the loop. That is the induced current is in a direction such that the induced magnetic field attempts to maintain the original flux through the loop. Go over Figure Induced emfs and Electric Fields A changing magnetic flux indices an emf and a current in a conducting loop. The current is due to an electric field setup by a battery, for example. Can also think of this as the following: a changing magnetic field creates an induced electric field. This electric field applies a force on the charges to cause them to move. 3

4 An electric field is created in a conductor as a result of changing magnetic flux - or - An electric field is always generated by a changing magnetic flux, even in free space where no charges are present. But the induced electric field has different properties to the electrostatic fields produced by stationary charges. Consider a conducting loop of radius r in a uniform magnetic field that is perpendiuclar to the plane of the loop. If the magnetic field changes with time, Faraday s law tells su that ɛ = dφ B /dt is induced in the loop. The induced current thus produced implies an induced electric field, E, that must be tangent to the loop so as to provide an electric force on the charges around the loop. The work done by the electric field on the loop in moving a test charge q once around the loop is W = qɛ. But the force on the charge is qe, and W = F.dr = qe(2πr). Equating these two expressions, we get E = ɛ 2πr. Using this result, together with faraday s law and Φ B = BA, we find E = r 2 db The negative sign indicates that the induced electric field E results in a current that opposes the change in the magnetic field. This result is valid in the absence of a conductor or charges. Thus the general form of Faraday s law of induction is ɛ = E.ds = dφ B The induced electric field E that appears above is a non-conservative field that is generated by a changing magnetic field. Its non-conservative because the work done in moving a charge around a closed path is not zero. Is this like an electrostatic filed? Self-Inductance Consider an isolated circuit consisting of a swicth, a resistor and a source of emf. 4

5 When the switch is closed, the current doesnt jump from zero to ɛ/r immediately. As the current increases with time, the magnetic flux through the loop of the circuit itself due to the current also increases with time. This increasing magnetic flux from the circuit induces an emf in the ciruit (back emf) that opposes the change in the net magnetic flux through the loop of the circuit. By Lenz s law, the induced electric field in the wires must therefore be opposite the direction of the current. the opposing emf results in a gradual increase in the emf. The emf setup in this case is called self-induced emf. From Faraday s law, the induced emf is the negative time rate of change of the magnetic flux. The magnetic flux is proportional to the magnetic field (why?), which in turn is proportional to the current in the circuit (why?). Thus the self induced emf is always proportional to the time rate of change of the current. More quantitatively, for a closely spaced coil of N turns, ɛ L = N dφ B dt = L di dt, where L is a proportionality constant called the inductance of the coil. The inductance of a coil containing N loops is L = NΦ B I. The inductance is the ratio, ɛ L L = di/ The SI unit of inductance is the henry (H): 1H = 1V.s/A. Inductance of a coil depends on geometry. A circuit that contains a coil, such as a solenoid, has a self-inductance that prevents the current from increasing or decreasing instantaneously. RL Circuits A circuit that contains a coil, such as a solenoid, has a self-inductance that prevents the current from increasing or decreasing instantaneously. A circuit element whose main purpose is to provide inductance in a circuit is called an inductor. Consider the circuit shown, consistin gof a resistor, an inductor, a swicth and a battery. 5

6 Ignore the resistance of the battery and suppose the switch is closed at t = 0. The current begins to increase, and due to the opposing current, the inductor produces an emf that opposes the increasing current. The back emf produced by the inductor is ɛ L = L di Applying Kirchoof s loop rule to the circuit: ɛ IR L di dt = 0, where IR is the voltage drop across the resistor. The potential difference across the inductor is given a negative sign because its emf is in the opposite sense to that of the battery. This is a differential equation. Its solution will give I(t). Can show the solution is I(t) = ɛ R (1 e t/τ ), where τ is the time constant of the RL circuit and τ = L/R. Dimension of τ is time. It is the time interval required for the current to reach (1 e 1 ) = of its final value ɛ/r. Note I(t) = 0 when t = 0. And at t = inf, I = ɛ/r. The final current, ɛ/r does not involve the inductance L because the inductor has no effect on the circuit if the current is not changing. Energy Stored in a Magnetic Field Induced emf set up by an inductor prevents a battery from establishing an instantaneous current. Part of the energy supplied by the batter goes into the internal energy in the resistor. The remaining energy is stored in the inductor. From Kirchoffls loop law, we have Iɛ = I 2 R + LI di This says that the rate, Iɛ, at which energy is supplied by the battery equals the rate, I 2 R, at which energy is delivered to the resistor and the rate, LI(dI/dt) at which energy is delivered to the inductor. 6

7 Thus, if U B is the energy stored in the inductor at any time, SOlving this, we get du B dt = LI di U B = 1 2 LI2, where L is constant. This is the energy stored in the magnetic field of the inductor when the current is I. Now consider a solenoid where L = µ 0 n 2 Al. The magnetic field of the solenoid is B = mu 0 ni. Then U B = 1 2 LI2 = 1 2 µ 0n 2 Al( B µ 0 n ) 2 = B2 2µ 0 (Al). Because Al is the volume of the solenoid, the energy stored per unit volume in a magnetic field, or the megnetic energy density, is u B = B2 1µ 0. This formula is valid for any region of space in which a magnetic field exists. Compare to eneergy per unit volume stored in an electric field, 1 2 ɛ 0E 2. 7

Induced voltages and Inductance Faraday s Law

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 information

Direction of Induced Current

Direction 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 information

Inductance. Motors. Generators

Inductance. Motors. Generators Inductance Motors Generators Self-inductance Self-inductance 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 information

Chapter 30 Inductance

Chapter 30 Inductance Chapter 30 Inductance - Mutual Inductance - Self-Inductance and Inductors - Magnetic-Field Energy - The R- Circuit - The -C Circuit - The -R-C Series Circuit . Mutual Inductance - A changing current in

More information

Physics 2220 Module 09 Homework

Physics 2220 Module 09 Homework Physics 2220 Module 09 Homework 01. A potential difference of 0.050 V is developed across the 10-cm-long wire of the figure as it moves though a magnetic field perpendicular to the page. What are the strength

More information

Solution Derivations for Capa #11

Solution 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 information

Chapter 11. Inductors ISU EE. C.Y. Lee

Chapter 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 information

Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering

Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering Homework #11 203-1-1721 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 information

ElectroMagnetic Induction. AP Physics B

ElectroMagnetic Induction. AP Physics B ElectroMagnetic Induction AP Physics B What is E/M Induction? Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a complete circuit, a current. Michael Faraday

More information

1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole.

1) 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 information

Fall 12 PHY 122 Homework Solutions #10

Fall 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 information

The purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.

The purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law. 260 17-1 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 information

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger

Slide 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 information

Physics 2102 Lecture 19. Physics 2102

Physics 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 information

Physics 126 Practice Exam #3 Professor Siegel

Physics 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 information

Chapter 14 Magnets and

Chapter 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 information

Module 22: Inductance and Magnetic Field Energy

Module 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 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. * 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

Chapter 20. Magnetic Induction Changing Magnetic Fields yield Changing Electric Fields

Chapter 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 information

Eðlisfræði 2, vor 2007

Eðlisfræði 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 information

March 20. Physics 272. Spring 2014 Prof. Philip von Doetinchem

March 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 information

Physics 1653 Exam 3 - Review Questions

Physics 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 information

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 self-inductance?

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 self-inductance? 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 self-inductance? From Equation 32-5, L = -E=(dI =dt) = 40 V=(100 A/s) = 0.4 H. 15. A cardboard

More information

Chapter 27 Electromagnetic Induction

Chapter 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 information

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao. D.C Machines

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao. D.C Machines D.C Machines 1 Introduction The steam age signalled the beginning of an industrial revolution. The advantages of machines and gadgets in helping mass production and in improving the services spurred the

More information

Inductance and Magnetic Energy

Inductance and Magnetic Energy Chapter 11 Inductance and Magnetic Energy 11.1 Mutual Inductance... 11-3 Example 11.1 Mutual Inductance of Two Concentric Coplanar Loops... 11-5 11. Self-Inductance... 11-5 Example 11. Self-Inductance

More information

Inductors & Inductance. Electronic Components

Inductors & 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 information

Lecture 22. Inductance. Magnetic Field Energy. Outline:

Lecture 22. Inductance. Magnetic Field Energy. Outline: Lecture 22. Inductance. Magnetic Field Energy. Outline: Self-induction and self-inductance. Inductance of a solenoid. The energy of a magnetic field. Alternative definition of inductance. Mutual Inductance.

More information

Chapter 27 Magnetic Field and Magnetic Forces

Chapter 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 information

1. 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. 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 information

Alternating Current RL Circuits

Alternating Current RL Circuits Alternating Current RL Circuits Objectives. To understand the voltage/current phase behavior of RL circuits under applied alternating current voltages, and. To understand the current amplitude behavior

More information

Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name

Phys222 Winter 2012 Quiz 4 Chapters 29-31. 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 information

Fall 12 PHY 122 Homework Solutions #8

Fall 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 information

Chapter 31: Induction and Inductance

Chapter 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 information

Physics 9 Fall 2009 Homework 8 - Solutions

Physics 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 information

Last time : energy storage elements capacitor.

Last 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 information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3. OUTCOME 3 - MAGNETISM and INDUCTION

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3. OUTCOME 3 - MAGNETISM and INDUCTION EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 3 - MAGNETISM and INDUCTION 3 Understand the principles and properties of magnetism Magnetic field:

More information

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49

Circuits 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

Objectives. Capacitors 262 CHAPTER 5 ENERGY

Objectives. 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 information

Magnetic Field of a Circular Coil Lab 12

Magnetic Field of a Circular Coil Lab 12 HB 11-26-07 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 information

Electromagnetic Induction

Electromagnetic 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 information

AP2 Magnetism. (c) Explain why the magnetic field does no work on the particle as it moves in its circular path.

AP2 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 information

Generate Electricity While Cycling

Generate Electricity While Cycling International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869, Volume-1, Issue-7, September 2013 Generate Electricity While Cycling Shubhankar Paul Abstract This paper will propose

More information

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13 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 information

Force on Moving Charges in a Magnetic Field

Force 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 information

Physics 112 Homework 5 (solutions) (2004 Fall) Solutions to Homework Questions 5

Physics 112 Homework 5 (solutions) (2004 Fall) Solutions to Homework Questions 5 Solutions to Homework Questions 5 Chapt19, Problem-2: (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 information

Exam 2 Solutions. PHY2054 Spring Prof. P. Kumar Prof. P. Avery March 5, 2008

Exam 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 information

Final Exam (40% of grade) on Monday December 7 th 1130a-230pm in York 2622 You can bring two 8.5x11 pages, front and back, of notes Calculators may

Final Exam (40% of grade) on Monday December 7 th 1130a-230pm in York 2622 You can bring two 8.5x11 pages, front and back, of notes Calculators may Final Exam (40% of grade) on Monday December 7 th 1130a-230pm in York 2622 You can bring two 8.5x11 pages, front and back, of notes Calculators may be used multiple choice like quizzes, only longer by

More information

Faraday s Law of Induction

Faraday s Law of Induction Chapter 10 Faraday s Law of Induction 10.1 Faraday s Law of Induction...10-10.1.1 Magnetic Flux...10-3 10.1. Lenz s Law...10-5 10. Motional EMF...10-7 10.3 Induced Electric Field...10-10 10.4 Generators...10-1

More information

University 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 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 information

Module P4.4 Electromagnetic induction

Module P4.4 Electromagnetic induction F L E X I B L E L E A R N I N G A P P R O A C H T O P H Y S I C S Module P4.4 Electromagnetic induction 1 Opening items 1.1 Module introduction 1.2 Fast track questions 1.3 Ready to study? 2 Introducing

More information

Problem 1 (25 points)

Problem 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 information

Chapter 7. Magnetism and Electromagnetism ISU EE. C.Y. Lee

Chapter 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 information

Chapter 10. Faraday s Law of Induction

Chapter 10. Faraday s Law of Induction 10 10 10-0 Chapter 10 Faraday s Law of Induction 10.1 Faraday s Law of Induction... 10-3 10.1.1 Magnetic Flux... 10-5 10.2 Motional EMF... 10-5 10.3 Faraday s Law (see also Faraday s Law Simulation in

More information

) 0.7 =1.58 10 2 N m.

) 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 information

Coupled Inductors. Introducing Coupled Inductors

Coupled Inductors. Introducing Coupled Inductors Coupled Inductors From power distribution across large distances to radio transmissions, coupled inductors are used extensively in electrical applications. Their properties allow for increasing or decreasing

More information

104 Practice Exam 2-3/21/02

104 Practice Exam 2-3/21/02 104 Practice Exam 2-3/21/02 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 non-zero

More information

Lecture 14. Magnetic Forces on Currents.

Lecture 14. Magnetic Forces on Currents. Lecture 14. Magnetic Forces on Currents. Outline: Hall Effect. Magnetic Force on a Wire Segment. Torque on a Current-Carrying Loop. Lecture 13: Magnetic Forces on Moving Charges - we considered individual

More information

Multiple Choice Questions for Physics 1 BA113 Chapter 23 Electric Fields

Multiple 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 information

Module 3 : Electromagnetism Lecture 13 : Magnetic Field

Module 3 : Electromagnetism Lecture 13 : Magnetic Field Module 3 : Electromagnetism Lecture 13 : Magnetic Field Objectives In this lecture you will learn the following Electric current is the source of magnetic field. When a charged particle is placed in an

More information

Electromagnetism Laws and Equations

Electromagnetism Laws and Equations Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E- and D-fields............................................. Electrostatic Force............................................2

More information

Chapter 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 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 information

Name: Date: Regents Physics Mr. Morgante UNIT 4B Magnetism

Name: 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 information

Scott 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. 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 information

Magnetic 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 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 information

Problem Solving 8: RC and LR Circuits

Problem Solving 8: RC and LR Circuits MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Problem Solving 8: RC and LR Circuits Section Table and Group (e.g. L04 3C ) Names Hand in one copy per group at the end of the Friday Problem

More information

MAGNETIC EFFECTS OF ELECTRIC CURRENT

MAGNETIC EFFECTS OF ELECTRIC CURRENT CHAPTER 13 MAGNETIC EFFECT OF ELECTRIC CURRENT In this chapter, we will study the effects of electric current : 1. Hans Christian Oersted (1777-1851) Oersted showed that electricity and magnetism are related

More information

Lesson 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. 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 information

April 1. Physics 272. Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html. Prof. Philip von Doetinchem philipvd@hawaii.

April 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 information

Chapter 4: DC Generators

Chapter 4: DC Generators Chapter 4: DC Generators Creating an AC Voltage The voltage produced in a DC generator is inherently AC and only becomes DC after rectification Consider an AC generator, consisting of a coil on the rotor

More information

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).

Edmund 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 information

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

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 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 information

NZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians

NZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers

More information

Physics 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. 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 information

physics 111N electric potential and capacitance

physics 111N electric potential and capacitance physics 111N electric potential and capacitance electric potential energy consider a uniform electric field (e.g. from parallel plates) note the analogy to gravitational force near the surface of the Earth

More information

MAGNETISM MAGNETISM. Principles of Imaging Science II (120)

MAGNETISM 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 information

Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.

Magnetism. 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 information

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

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 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 information

Chapter 25 Practice Problems, Review, and Assessment

Chapter 25 Practice Problems, Review, and Assessment Chapter 25 Practice Problems, Review, and Assessment Section 1 Inducing Currents: Practice Problems 1. You move a straight wire that is 0.5 m long at a speed of 20 m/s vertically through a 0.4-T magnetic

More information

1. Title Electrical fundamentals II (Mechanics Repair and Maintenance)

1. Title Electrical fundamentals II (Mechanics Repair and Maintenance) 1. Title Electrical fundamentals II (Mechanics Repair and Maintenance) 2. Code EMAMBG429A 3. Range The knowledge is needed for a wide range of aircraft repair and maintenance works,e.g. applicable to aircrafts,

More information

" - angle between l and a R

 - 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 information

HOMEWORK #9 MAGNETIC FIELD, ELECTROMAGNETIC INDUCTION, CHAPTER 27

HOMEWORK #9 MAGNETIC FIELD, ELECTROMAGNETIC INDUCTION, CHAPTER 27 HOEWORK #9 AGNETC FELD, ELECTROAGNETC NDUCTON, CHAPTER 7 54 A long tungsten-core solenoid carries a current. (a) f the core is reoved while the current is held constant, does the agnetic field strength

More information

Physics 9 Fall 2009 Homework 7 - Solutions

Physics 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 information

Last Name: First Name: Physics 102 Spring 2006: Exam #2 Multiple-Choice Questions 1. A charged particle, q, is moving with speed v perpendicular to a uniform magnetic field. A second identical charged

More information

Question Details C14: Magnetic Field Direction Abbott [ ]

Question 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 information

Reading assignment: All students should read the Appendix about using oscilloscopes.

Reading assignment: All students should read the Appendix about using oscilloscopes. 10. A ircuits* Objective: To learn how to analyze current and voltage relationships in alternating current (a.c.) circuits. You will use the method of phasors, or the vector addition of rotating vectors

More information

Question Bank. 1. Electromagnetism 2. Magnetic Effects of an Electric Current 3. Electromagnetic Induction

Question 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 information

Candidate Number. General Certificate of Education Advanced Level Examination June 2010

Candidate Number. General Certificate of Education Advanced Level Examination June 2010 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 1 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Friday 18

More information

RUPHYS2272015 ( RUPHY227F2015 ) My Courses Course Settings University Physics with Modern Physics, 14e Young/Freedman

RUPHYS2272015 ( 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 information

Solution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are:

Solution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are: Problem 1. (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields as shown in the figure. (b) Repeat part (a), assuming the moving particle is

More information

EEE1001/PHY1002. Magnetic Circuits. The circuit is of length l=2πr. B andφ circulate

EEE1001/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 information

Physics 25 Exam 3 November 3, 2009

Physics 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 information

CHARGE TO MASS RATIO OF THE ELECTRON

CHARGE TO MASS RATIO OF THE ELECTRON CHARGE TO MASS RATIO OF THE ELECTRON In solving many physics problems, it is necessary to use the value of one or more physical constants. Examples are the velocity of light, c, and mass of the electron,

More information

PHYS 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. 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 information

Digital Energy ITI. Instrument Transformer Basic Technical Information and Application

Digital Energy ITI. Instrument Transformer Basic Technical Information and Application g Digital Energy ITI Instrument Transformer Basic Technical Information and Application Table of Contents DEFINITIONS AND FUNCTIONS CONSTRUCTION FEATURES MAGNETIC CIRCUITS RATING AND RATIO CURRENT TRANSFORMER

More information

CET Moving Charges & Magnetism

CET 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 information

EE 221 Circuits II. Chapter 13 Magnetically Coupled Circuits

EE 221 Circuits II. Chapter 13 Magnetically Coupled Circuits EE Circuits II Chapter 3 Magnetically Coupled Circuits Magnetically Coupled Circuits 3. What is a transformer? 3. Mutual Inductance 3.3 Energy in a Coupled Circuit 3.4 inear Transformers 3.5 Ideal Transformers

More information

Chapter 4. Magnetic Materials and Circuits

Chapter 4. Magnetic Materials and Circuits Chapter 4 Magnetic Materials and Circuits Objectives List six characteristics of magnetic field. Understand the right-hand rule for current and magnetic fluxes. Define magnetic flux, flux density, magnetomotive

More information

TEACHER S CLUB EXAMS GRADE 11. PHYSICAL SCIENCES: PHYSICS Paper 1

TEACHER S CLUB EXAMS GRADE 11. PHYSICAL SCIENCES: PHYSICS Paper 1 TEACHER S CLUB EXAMS GRADE 11 PHYSICAL SCIENCES: PHYSICS Paper 1 MARKS: 150 TIME: 3 hours INSTRUCTIONS AND INFORMATION 1. This question paper consists of 12 pages, two data sheets and a sheet of graph

More information