Chapter 21 Magnetic Induction Lecture 12

Size: px
Start display at page:

Download "Chapter 21 Magnetic Induction Lecture 12"

Transcription

1 Chapter 21 Magnetic Induction Lecture Why is it called Electromagnetism? 21.2 Magnetic Flux and Faraday s Law 21.3 Lenz s Law and Work-Energy Principles 21.4 Inductance 21.5 RL Circuits 21.6 Energy Stored in a Magnetic Field

2 Electromagnetism and Magnetic Induction Electric and magnetic phenomena were connected by Ørsted in 1820 He discovered an electric current in a wire can exert a force on a compass needle Indicated a electric field can lead to a force on a magnet He concluded an electric field can produce a magnetic field Did a magnetic field produce an electric field? Yes! Experiments were done by Michael Faraday This effect is called magnetic induction This links electricity and magnetism in a fundamental way Section 21.1

3 Faraday s Experiment Faraday attempted to observe an induced electric field He used an ammeter instead of a light bulb If the bar magnet was in motion, a current was observed If the magnet is stationary, the current and the electric field are both zero Section 21.1

4 Another Faraday Experiment A solenoid is positioned near a loop of wire with the light bulb He passed a current through the solenoid by connecting it to a battery When the current through the solenoid is constant, there is no current in the wire When the switch is opened or closed, the bulb does light up Section 21.1

5 Conclusions from Experiments An electric current is produced during those instances when the current through the solenoid is changing Faraday s experiments show that an electric current is produced in the wire loop only when the magnetic field at the loop is changing A changing magnetic field produces an electric field An electric field produced in this way is called an induced electric field The phenomena is called electromagnetic induction Section 21.1

6 Magnetic Flux Faraday developed a quantitative theory of induction now called Faraday s Law The law shows how to calculate the induced electric field in different situations Faraday s Law uses the concept of magnetic flux Magnetic flux is similar to the concept of electric flux Let A be an area of a surface with a magnetic field passing through it The flux is Φ B = B A cos θ Section 21.2

7 Magnetic Flux, cont. If the field is perpendicular to the surface, Φ B = B A If the field makes an angle θ with the normal to the surface, Φ B = B A cos θ If the field is parallel to the surface, Φ B = 0 The SI unit of magnetic flux is the Weber (Wb) 1 Wb = 1 T. m 2 Section 21.2

8 Faraday s Law Faraday s Law indicates how to calculate the potential difference that produces the induced current Written in terms of the electromotive force induced in the wire loop t Φ B = B A cos θ The magnitude of the induced emf equals the rate of change of the magnetic flux The negative sign is Lenz s Law B Section 21.2

9 Applying Faraday s Law The ε is the induced emf in the wire loop Its value will be indicated on the voltmeter It is related to the electric field directly along and inside the wire loop The induced potential difference produces the current

10 Flux Though a Changing Area A magnetic field is constant and in a direction perpendicular to the plane of the rails and the bar Assume the bar moves at a constant speed The magnitude of the induced emf is ε = B L v Φ B = B A cos θ t The current leads to power dissipation in the circuit (by the resistor) Section 21.2 B

11 Conservation of Energy The mechanical power put into the bar by the external agent is equal to the electrical power delivered to the resistor Energy is converted from mechanical to electrical, but the total energy remains the same Conservation of energy is obeyed by electromagnetic phenomena Section 21.2

12 Electrical Generator Need to make the rate of change of the flux large enough to give a useful emf t B Φ B = B A cos θ Use rotational motion instead of linear motion A permanent magnet produces a constant magnetic field in the region between its poles Section 21.2

13 Changing a Magnetic Flux, Summary Section 21.2

14 Lenz s Law Lenz s Law gives an easy way to determine the sign of the induced emf Lenz s Law states the magnetic field produced by an induced current always opposes any changes in the magnetic flux Φ B = B A cos θ t B Section 21.3

15 Lenz s Law, Example 1 Assume a metal loop in which the magnetic field passes upward through it Assume the magnetic flux increases with time The magnetic field produced by the induced emf must oppose the change in flux Therefore, the induced magnetic field must be downward and the induced current will be clockwise Section 21.3

16 Lenz s Law, Example 2 Assume a metal loop in which the magnetic field passes upward through it Assume the magnetic flux decreases with time The magnetic field produced by the induced emf must oppose the change in flux Therefore, the induced magnetic field must be upward and the induced current will be counterclockwise Section 21.3

17 Inductance In some cases, you must include the induced flux When the switch is closed, a sudden change in current occurs in the coil This current produces a magnetic field An emf and current are induced in the coil t B Section 21.4

18 Inductor A coil is type of circuit element called an inductor Many inductors are constructed as small solenoids Almost any coil or loop will act as an inductor Whenever the current through an inductor changes, a voltage is induced in the inductor that opposes this change This phenomenon is called self-inductance The current changing through a coil induces a current in the same coil The induced current opposes the original applied current, from Lenz s Law Section 21.4

19 Inductance of a Solenoid Faraday s Law can be used to find the inductance of a solenoid N B BAcos, B o I o L is the symbol for inductance L NA 2 l The voltage across the solenoid can be expressed in terms of the inductance I L V t emf,l d N B d Li L di dt dt dt The results apply to all coils or loops of wire The value of L depends on the physical size and shape of the circuit element The voltage drop across an inductor is The unit of inductance is the Henry 1 H = 1 V. s / A I VL L t t Section 21.4 B

20 Mutual Inductance It is possible for the magnetic field of one coil to produce an induced current in a second coil The coils are connected indirectly through the magnetic flux The effect is called mutual inductance Section 21.4

21 RL Circuit DC circuits may contain resistors, inductors, and capacitors The voltage source is a battery or some other source that provides a constant voltage across its output terminals Behavior of DC circuits with inductors Immediately after any switch is closed or opened, the induced emfs keep the current through all inductors equal to the values they had the instant before the switch was thrown After a switch has been closed or opened for a very long time, the induced emfs are zero Section 21.5

22 RL Circuit Example t B Section 21.5

23 RL Circuit Example, Analysis The presence of resistors and an inductor make the circuit an RL circuit The current starts at zero since the switch has been open for a very long time At t = 0, the switch is closed, inducing a potential across the inductor Just after t = 0, the current in the second loop is zero After the switch has been closed for a long time, the voltage across the inductor is zero Section 21.5

24 Time Constant for RL Circuit The current at time t is found by V t I e R 1 is called the time constant of the circuit For a single resistor in series with a single inductor, L R The voltage is given by VL Ve t Section 21.5

25 Real Inductors Most practical inductors are constructed by wrapping a wire coil around a magnetic material Filling a coil with magnetic material greatly increases the magnetic flux through the coil and therefore increases the induced emf The presence of magnetic material increases the inductance Most inductors contain a magnetic material inside which produces a larger value of L in a smaller package Section 21.5

26 Energy in an Inductor Energy is stored in the magnetic field of an inductor The energy stored in an inductor is PE ind = ½ L I 2 Very similar in form to the energy stored in the electric field of a capacitor The expression for energy can also be stated as PE ind 1 NA I 2 2 o In terms of the magnetic field, 1 PEmag B 2 volume 2 o 2 Section 21.6

27 Energy in an Inductor, cont. Energy contained in the magnetic field actually exists anywhere there is a magnetic field, not just in a solenoid Can exist in empty space The potential energy can also be expressed in terms of the energy density in the magnetic field PEmag 1 2 energy density umag B volume 2 o This expression is similar to the energy density contained in an electric field Section 21.6

28 Demo: Jumping Rings (1) 28

ELECTROMAGNETIC INDUCTION AND FARADAY S LAW

ELECTROMAGNETIC INDUCTION AND FARADAY S LAW ELECTROMAGNETIC INDUCTION AND FARADAY S LAW Magnetic Flux The emf is actually induced by a change in the quantity called the magnetic flux rather than simply py by a change in the magnetic field Magnetic

More information

Induction and inductance

Induction and inductance PH -C Fall 01 Induction and inductance Lecture 15 Chapter 30 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th etion) 1 Chapter 30 Induction and Inductance In this chapter we will study the following

More information

Induction and Inductance

Induction and Inductance Induction and Inductance Key Contents Faraday s law: induced emf Induction and energy transfer Inductors and inductance RL circuits Magnetic energy density The First Experiment 1. A current appears only

More information

Chapter 30. Induction and Inductance

Chapter 30. Induction and Inductance Chapter 30 Induction and Inductance 30.2: First Experiment: 1. A current appears only if there is relative motion between the loop and the magnet (one must move relative to the other); the current disappears

More information

Electricity & Optics

Electricity & Optics Physics 24100 Electricity & Optics Lecture 16 Chapter 28 sec. 1-3 Fall 2017 Semester Professor Koltick Magnetic Flux We define magnetic flux in the same way we defined electric flux: φ e = n E da φ m =

More information

Electromagnetic Induction (Chapters 31-32)

Electromagnetic Induction (Chapters 31-32) Electromagnetic Induction (Chapters 31-3) The laws of emf induction: Faraday s and Lenz s laws Inductance Mutual inductance M Self inductance L. Inductors Magnetic field energy Simple inductive circuits

More information

Chapter 30. Induction and Inductance

Chapter 30. Induction and Inductance Chapter 30 Induction and Inductance 30.2: First Experiment: 1. A current appears only if there is relative motion between the loop and the magnet (one must move relative to the other); the current disappears

More information

PHYSICS Fall Lecture 15. Electromagnetic Induction and Faraday s Law

PHYSICS Fall Lecture 15. Electromagnetic Induction and Faraday s Law PHYSICS 1444-001 Fall 2012 Lecture 15 Electromagnetic Induction and Faraday s Law A current can be produced by a changing magnetic field First shown in an experiment by Michael Faraday Induced emf A primary

More information

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Lesson 7 Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit Alternating Current Electromagnetic

More information

PHYS 202 Notes, Week 6

PHYS 202 Notes, Week 6 PHYS 202 Notes, Week 6 Greg Christian February 23 & 25, 2016 Last updated: 02/25/2016 at 12:36:40 This week we learn about electromagnetic induction. Magnetic Induction This section deals with magnetic

More information

Chapter 23 Magnetic Flux and Faraday s Law of Induction

Chapter 23 Magnetic Flux and Faraday s Law of Induction Chapter 23 Magnetic Flux and Faraday s Law of Induction Recall: right hand rule 2 10/28/2013 Units of Chapter 23 Induced Electromotive Force Magnetic Flux Faraday s Law of Induction Lenz s Law Mechanical

More information

PHYSICS. Chapter 30 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT

PHYSICS. Chapter 30 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 30 Lecture RANDALL D. KNIGHT Chapter 30 Electromagnetic Induction IN THIS CHAPTER, you will learn what electromagnetic induction is

More information

Chapter 30. Inductance

Chapter 30. Inductance Chapter 30 Inductance Self Inductance When a time dependent current passes through a coil, a changing magnetic flux is produced inside the coil and this in turn induces an emf in that same coil. This induced

More information

Chapter 23 Magnetic Flux and Faraday s Law of Induction

Chapter 23 Magnetic Flux and Faraday s Law of Induction Chapter 23 Magnetic Flux and Faraday s Law of Induction 1 Overview of Chapter 23 Induced Electromotive Force Magnetic Flux Faraday s Law of Induction Lenz s Law Mechanical Work and Electrical Energy Generators

More information

Can a Magnetic Field Produce a Current?

Can a Magnetic Field Produce a Current? Can a Magnetic Field Produce a Current? In our study of magnetism we learned that an electric current through a wire, or moving electrically charged objects, produces a magnetic field. Could the reverse

More information

Recap (1) Maxwell s Equations describe the electric field E and magnetic field B generated by stationary charge density ρ and current density J:

Recap (1) Maxwell s Equations describe the electric field E and magnetic field B generated by stationary charge density ρ and current density J: Class 13 : Induction Phenomenon of induction and Faraday s Law How does a generator and transformer work? Self- and mutual inductance Energy stored in B-field Recap (1) Maxwell s Equations describe the

More information

Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies

Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies Induced emf - Faraday s Experiment When a magnet moves toward a loop of wire, the ammeter shows the presence of a current When

More information

Chapter 5: Electromagnetic Induction

Chapter 5: Electromagnetic Induction Chapter 5: Electromagnetic Induction 5.1 Magnetic Flux 5.1.1 Define and use magnetic flux Magnetic flux is defined as the scalar product between the magnetic flux density, B with the vector of the area,

More information

Sliding Conducting Bar

Sliding Conducting Bar Motional emf, final For equilibrium, qe = qvb or E = vb A potential difference is maintained between the ends of the conductor as long as the conductor continues to move through the uniform magnetic field

More information

PHYSICS - GIANCOLI CALC 4E CH 29: ELECTROMAGNETIC INDUCTION.

PHYSICS - GIANCOLI CALC 4E CH 29: ELECTROMAGNETIC INDUCTION. !! www.clutchprep.com CONCEPT: ELECTROMAGNETIC INDUCTION A coil of wire with a VOLTAGE across each end will have a current in it - Wire doesn t HAVE to have voltage source, voltage can be INDUCED i V Common

More information

Physics 6B Summer 2007 Final

Physics 6B Summer 2007 Final Physics 6B Summer 2007 Final Question 1 An electron passes through two rectangular regions that contain uniform magnetic fields, B 1 and B 2. The field B 1 is stronger than the field B 2. Each field fills

More information

Faraday's Law ds B B G G ΦB B ds Φ ε = d B dt

Faraday's Law ds B B G G ΦB B ds Φ ε = d B dt Faraday's Law ds ds ε= d Φ dt Φ Global Review Electrostatics» motion of q in external E-field» E-field generated by Σq i Magnetostatics» motion of q and i in external -field» -field generated by I Electrodynamics»

More information

Electromagnetic Induction. Bo Zhou Faculty of Science, Hokudai

Electromagnetic Induction. Bo Zhou Faculty of Science, Hokudai Electromagnetic Induction Bo Zhou Faculty of Science, Hokudai Oersted's law Oersted s discovery in 1820 that there was a close connection between electricity and magnetism was very exciting until then,

More information

Can a Magnetic Field Produce a Current?

Can a Magnetic Field Produce a Current? Can a Magnetic Field Produce a Current? In our study of magnetism we learned that an electric current through a wire, or moving electrically charged objects, produces a magnetic field. Could the reverse

More information

Chapter 27, 28 & 29: Magnetism & Electromagnetic Induction. Magnetic flux Faraday s and Lenz s law Electromagnetic Induction Ampere s law

Chapter 27, 28 & 29: Magnetism & Electromagnetic Induction. Magnetic flux Faraday s and Lenz s law Electromagnetic Induction Ampere s law Chapter 27, 28 & 29: Magnetism & Electromagnetic Induction Magnetic flux Faraday s and Lenz s law Electromagnetic Induction Ampere s law 1 Magnetic Flux and Faraday s Law of Electromagnetic Induction We

More information

College Physics B - PHY2054C

College Physics B - PHY2054C Force on a Torque on a College - PHY2054C & 09/29/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building Outline Force on a Torque on a 1 Force on a Torque on a 2 3 4 Force on a Torque on a Force

More information

INDUCTANCE Self Inductance

INDUCTANCE Self Inductance NDUTANE 3. Self nductance onsider the circuit shown in the Figure. When the switch is closed the current, and so the magnetic field, through the circuit increases from zero to a specific value. The increasing

More information

Electromagnetic Induction & Inductors

Electromagnetic Induction & Inductors Electromagnetic Induction & Inductors 1 Revision of Electromagnetic Induction and Inductors (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) Magnetic Field

More information

P202 Practice Exam 2 Spring 2004 Instructor: Prof. Sinova

P202 Practice Exam 2 Spring 2004 Instructor: Prof. Sinova P202 Practice Exam 2 Spring 2004 Instructor: Prof. Sinova Name: Date: (5)1. How many electrons flow through a battery that delivers a current of 3.0 A for 12 s? A) 4 B) 36 C) 4.8 10 15 D) 6.4 10 18 E)

More information

Chapter 23: Magnetic Flux and Faraday s Law of Induction

Chapter 23: Magnetic Flux and Faraday s Law of Induction Chapter 3: Magnetic Flux and Faraday s Law of Induction Answers Conceptual Questions 6. Nothing. In this case, the break prevents a current from circulating around the ring. This, in turn, prevents the

More information

DO PHYSICS ONLINE MOTORS AND GENERATORS FARADAY S LAW ELECTROMAGNETIC INDUCTION

DO PHYSICS ONLINE MOTORS AND GENERATORS FARADAY S LAW ELECTROMAGNETIC INDUCTION DO PHYSICS ONLINE MOTORS AND GENERATORS FARADAY S LAW ELECTROMAGNETIC INDUCTION English Michael Faraday (1791 1867) who experimented with electric and magnetic phenomena discovered that a changing magnetic

More information

Agenda for Today. Elements of Physics II. Forces on currents

Agenda for Today. Elements of Physics II. Forces on currents Forces on currents Physics 132: Lecture e 14 Elements of Physics II Agenda for Today Currents are moving charges Torque on current loop Torque on rotated loop Currents create B-fields Adding magnetic fields

More information

LECTURE 17. Reminder Magnetic Flux

LECTURE 17. Reminder Magnetic Flux LECTURE 17 Motional EMF Eddy Currents Self Inductance Reminder Magnetic Flux Faraday s Law ε = dφ B Flux through one loop Φ B = BAcosθ da Flux through N loops Φ B = NBAcosθ 1 Reminder How to Change Magnetic

More information

Electromagnetic Induction

Electromagnetic Induction Electromagnetic Induction Name Section Theory Electromagnetic induction employs the concept magnetic flux. Consider a conducting loop of area A in a magnetic field with magnitude B. The flux Φ is proportional

More information

Handout 10: Inductance. Self-Inductance and inductors

Handout 10: Inductance. Self-Inductance and inductors 1 Handout 10: Inductance Self-Inductance and inductors In Fig. 1, electric current is present in an isolate circuit, setting up magnetic field that causes a magnetic flux through the circuit itself. This

More information

PHYS 1442 Section 004 Lecture #14

PHYS 1442 Section 004 Lecture #14 PHYS 144 Section 004 Lecture #14 Wednesday March 5, 014 Dr. Chapter 1 Induced emf Faraday s Law Lenz Law Generator 3/5/014 1 Announcements After class pickup test if you didn t Spring break Mar 10-14 HW7

More information

Lecture 10 Induction and Inductance Ch. 30

Lecture 10 Induction and Inductance Ch. 30 Lecture 10 Induction and Inductance Ch. 30 Cartoon - Faraday Induction Opening Demo - Thrust bar magnet through coil and measure the current Topics Faraday s Law Lenz s Law Motional Emf Eddy Currents LR

More information

Faraday s Law; Inductance

Faraday s Law; Inductance This test covers Faraday s Law of induction, motional emf, Lenz s law, induced emf and electric fields, eddy currents, self-inductance, inductance, RL circuits, and energy in a magnetic field, with some

More information

Part 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is

Part 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is 1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field

More information

Last time. Ampere's Law Faraday s law

Last time. Ampere's Law Faraday s law Last time Ampere's Law Faraday s law 1 Faraday s Law of Induction (More Quantitative) The magnitude of the induced EMF in conducting loop is equal to the rate at which the magnetic flux through the surface

More information

Electromagnetic Induction

Electromagnetic Induction Electromagnetic Induction PHY232 Remco Zegers zegers@nscl.msu.edu Room W109 cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html previously: electric currents generate magnetic field. If a current

More information

CHAPTER 5: ELECTROMAGNETIC INDUCTION

CHAPTER 5: ELECTROMAGNETIC INDUCTION CHAPTER 5: ELECTROMAGNETIC INDUCTION PSPM II 2005/2006 NO. 5 5. An AC generator consists a coil of 30 turns with cross sectional area 0.05 m 2 and resistance 100 Ω. The coil rotates in a magnetic field

More information

AP Physics C - E & M

AP Physics C - E & M AP Physics C - E & M Electromagnetic Induction 2017-07-14 www.njctl.org Table of Contents: Electromagnetic Induction Click on the topic to go to that section. Induced EMF Magnetic Flux and Gauss's Law

More information

FARADAY S AND LENZ LAW B O O K P G

FARADAY S AND LENZ LAW B O O K P G FARADAY S AND LENZ LAW B O O K P G. 4 3 6-438 MOTIONAL EMF AND MAGNETIC FLUX (DERIVIATION) Motional emf = vbl Let a conducting rod being moved through a magnetic field B During time t 0 the rod has been

More information

Chapter 5. Electromagnetic Induction

Chapter 5. Electromagnetic Induction Chapter 5 Electromagnetic Induction Overview In the last chapter, we studied how a current produces a magnetic field. Here we will study the reverse effect: A magnetic field can produce an electric field

More information

General Physics II. Electromagnetic Induction and Electromagnetic Waves

General Physics II. Electromagnetic Induction and Electromagnetic Waves General Physics II Electromagnetic Induction and Electromagnetic Waves 1 Induced emf We have seen that an electric current produces a magnetic field. Michael Faraday demonstrated that a magnetic field

More information

Motional EMF & Lenz law

Motional EMF & Lenz law Phys 102 Lecture 13 Motional EMF & Lenz law 1 Physics 102 recently Basic principles of magnetism Lecture 10 magnetic fields & forces Lecture 11 magnetic dipoles & current loops Lecture 12 currents & magneticfields

More information

Chapter 20: Electromagnetic Induction. PHY2054: Chapter 20 1

Chapter 20: Electromagnetic Induction. PHY2054: Chapter 20 1 Chapter 20: Electromagnetic Induction PHY2054: Chapter 20 1 Electromagnetic Induction Magnetic flux Induced emf Faraday s Law Lenz s Law Motional emf Magnetic energy Inductance RL circuits Generators and

More information

Faraday s Law. Lecture 17. Chapter 33. Physics II. Course website:

Faraday s Law. Lecture 17. Chapter 33. Physics II. Course website: Lecture 17 Chapter 33 Physics II Faraday s Law Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html Electromagnetic

More information

Induction_P1. 1. [1 mark]

Induction_P1. 1. [1 mark] Induction_P1 1. [1 mark] Two identical circular coils are placed one below the other so that their planes are both horizontal. The top coil is connected to a cell and a switch. The switch is closed and

More information

Faraday s Law. Lecture 17. Chapter 33. Physics II. Course website:

Faraday s Law. Lecture 17. Chapter 33. Physics II. Course website: Lecture 17 Chapter 33 Physics II Faraday s Law Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Electromagnetic induction We saw that a magnetic field could be produced with an

More information

Electromagnetic Induction

Electromagnetic Induction Chapter II Electromagnetic Induction Day 1 Induced EMF, Faraday s Law and Lenz s Law Sections 21-1 to 21-2 Electromotive Force Electromotive force (EMF ore) is a misnomer, as it is not really a force but

More information

Magnetic flux. where θ is the angle between the magnetic field and the area vector. The unit of magnetic flux is the weber. 1 Wb = 1 T m 2.

Magnetic flux. where θ is the angle between the magnetic field and the area vector. The unit of magnetic flux is the weber. 1 Wb = 1 T m 2. Magnetic flux Magnetic flux is a measure of the number of magnetic field lines passing through something, such as a loop. If we define the area of the loop as a vector, with its direction perpendicular

More information

21 MAGNETIC FORCES AND MAGNETIC FIELDS

21 MAGNETIC FORCES AND MAGNETIC FIELDS CHAPTER 1 MAGNETIC FORCES AND MAGNETIC FIELDS ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1 (d) Right-Hand Rule No 1 gives the direction of the magnetic force as x for both drawings A and B In drawing C, the

More information

Physics 54 Lecture March 1, Micro-quiz problems (magnetic fields and forces) Magnetic dipoles and their interaction with magnetic fields

Physics 54 Lecture March 1, Micro-quiz problems (magnetic fields and forces) Magnetic dipoles and their interaction with magnetic fields Physics 54 Lecture March 1, 2012 OUTLINE Micro-quiz problems (magnetic fields and forces) Magnetic dipoles and their interaction with magnetic fields Electromagnetic induction Introduction to electromagnetic

More information

mag ( ) 1 ). Since I m interested in the magnitude of the flux, I ll avoid the minus sign by taking the normal to point upward.

mag ( ) 1 ). Since I m interested in the magnitude of the flux, I ll avoid the minus sign by taking the normal to point upward. hysics 40 Homework olutions - Walker Chapter 3 Conceptual Questions CQ5. Before the switch is closed there is no current in the coil and therefore no netic flux through the metal ring. When the switch

More information

Induction and Inductance

Induction and Inductance Welcome Back to Physics 1308 Induction and Inductance Michael Faraday 22 September 1791 25 August 1867 Announcements Assignments for Tuesday, November 6th: - Reading: Chapter 30.6-30.8 - Watch Videos:

More information

Last Homework. Reading: Chap. 33 and Chap. 33. Suggested exercises: 33.1, 33.3, 33.5, 33.7, 33.9, 33.11, 33.13, 33.15,

Last Homework. Reading: Chap. 33 and Chap. 33. Suggested exercises: 33.1, 33.3, 33.5, 33.7, 33.9, 33.11, 33.13, 33.15, Chapter 33. Electromagnetic Induction Electromagnetic induction is the scientific principle that underlies many modern technologies, from the generation of electricity to communications and data storage.

More information

Electromagnetism Notes 1 Magnetic Fields

Electromagnetism Notes 1 Magnetic Fields Electromagnetism Notes 1 Magnetic Fields Magnets can or other magnets. They are able to exert forces on each other without touching because they are surrounded by. Magnetic Flux refers to Areas with many

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 2140) Lecture 10 6/12/2007 Electricity and Magnetism Induced voltages and induction Self-Inductance RL Circuits Energy in magnetic fields AC circuits and EM waves Resistors, capacitors

More information

Chapter 21 Lecture Notes

Chapter 21 Lecture Notes Chapter 21 Lecture Notes Physics 2424 - Strauss Formulas: Φ = BA cosφ E = -N Φ/ t Faraday s Law E = Bvl E = NABω sinωt M = (N 2 Φ 2 )/I 1 E 2 = -M I 1 / t L = NΦ/I E = -L I/ t L = µ 0 n 2 A l Energy =

More information

Magnetism. and its applications

Magnetism. and its applications Magnetism and its applications Laws of Magnetism 1) Like magnetic poles repel, and 2) unlike poles attract. Magnetic Direction and Strength Law 3 - Magnetic force, either attractive or repelling varies

More information

PHY 1214 General Physics II

PHY 1214 General Physics II PHY 1214 General Physics II Lecture 19 Induced EMF and Motional EMF July 5-6, 2005 Weldon J. Wilson Professor of Physics & Engineering Howell Hall 221H wwilson@ucok.edu Lecture Schedule (Weeks 4-6) We

More information

Chapter 22. Induction

Chapter 22. Induction Chapter 22 Induction Induced emf A current can be produced by a changing magnetic field First shown in an experiment by Michael Faraday A primary coil is connected to a battery A secondary coil is connected

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Induction Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 25! Last week we learned that a current-carrying loop in a magnetic field experiences a torque! If we start with a loop with

More information

PHYS 1444 Section 003 Lecture #18

PHYS 1444 Section 003 Lecture #18 PHYS 1444 Section 003 Lecture #18 Wednesday, Nov. 2, 2005 Magnetic Materials Ferromagnetism Magnetic Fields in Magnetic Materials; Hysteresis Induced EMF Faraday s Law of Induction Lenz s Law EMF Induced

More information

Demo: Solenoid and Magnet. Topics. Chapter 22 Electromagnetic Induction. EMF Induced in a Moving Conductor

Demo: Solenoid and Magnet. Topics. Chapter 22 Electromagnetic Induction. EMF Induced in a Moving Conductor Topics Chapter 22 Electromagnetic Induction EMF Induced in a Moving Conductor Magnetic Flux EMF Induced in a Moving Conductor Demo: Solenoid and Magnet v 1 EMF Induced in a Moving Conductor q Work done

More information

PRACTICE EXAM 1 for Midterm 2

PRACTICE EXAM 1 for Midterm 2 PRACTICE EXAM 1 for Midterm 2 Multiple Choice Questions 1) The figure shows three identical lightbulbs connected to a battery having a constant voltage across its terminals. What happens to the brightness

More information

AP Physics C Unit 11: Electromagnetic Induction. Part 1 - Faraday s Law and Lenz s Law

AP Physics C Unit 11: Electromagnetic Induction. Part 1 - Faraday s Law and Lenz s Law AP Physics C Unit 11: Electromagnetic Induction Part 1 - Faraday s Law and Lenz s Law What is E/M Induction? Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in

More information

Chapter 12. Magnetism and Electromagnetism

Chapter 12. Magnetism and Electromagnetism Chapter 12 Magnetism and Electromagnetism 167 168 AP Physics Multiple Choice Practice Magnetism and Electromagnetism SECTION A Magnetostatics 1. Four infinitely long wires are arranged as shown in the

More information

K2-04: FARADAY'S EXPERIMENT - EME K2-43: LENZ'S LAW - PERMANENT MAGNET AND COILS

K2-04: FARADAY'S EXPERIMENT - EME K2-43: LENZ'S LAW - PERMANENT MAGNET AND COILS K2-04: FARADAY'S EXPERIMENT - EME SET - 20, 40, 80 TURN COILS K2-62: CAN SMASHER - ELECTROMAGNETIC K2-43: LENZ'S LAW - PERMANENT MAGNET AND COILS K2-44: EDDY CURRENT PENDULUM K4-06: MAGNETOELECTRIC GENERATOR

More information

Inductance, RL and RLC Circuits

Inductance, RL and RLC Circuits Inductance, RL and RLC Circuits Inductance Temporarily storage of energy by the magnetic field When the switch is closed, the current does not immediately reach its maximum value. Faraday s law of electromagnetic

More information

Electricity & Magnetism

Electricity & Magnetism Ch 31 Faraday s Law Electricity & Magnetism Up to this point, we ve seen electric fields produced by electric charges... E =... and magnetic fields produced by moving charges... k dq E da = q in r 2 B

More information

Chapters 34,36: Electromagnetic Induction. PHY2061: Chapter

Chapters 34,36: Electromagnetic Induction. PHY2061: Chapter Chapters 34,36: Electromagnetic Induction PHY2061: Chapter 34-35 1 Electromagnetic Induction Magnetic flux Induced emf Faraday s Law Lenz s Law Motional emf Magnetic energy Inductance RL circuits Generators

More information

Physics 1302W.400 Lecture 33 Introductory Physics for Scientists and Engineering II

Physics 1302W.400 Lecture 33 Introductory Physics for Scientists and Engineering II Physics 1302W.400 Lecture 33 Introductory Physics for Scientists and Engineering II In today s lecture, we will discuss generators and motors. Slide 30-1 Announcement Quiz 4 will be next week. The Final

More information

Version 001 HW 22 EM Induction C&J sizemore (21301jtsizemore) 1

Version 001 HW 22 EM Induction C&J sizemore (21301jtsizemore) 1 Version 001 HW 22 EM Induction C&J sizemore (21301jtsizemore) 1 This print-out should have 35 questions. Multiple-choice questions may continue on the next column or page find all choices before answering.

More information

Electromagnetic Induction

Electromagnetic Induction lectromagnetic Induction Induced MF We already know that moving charge (=current) causes magnetic field It also works the other way around: changing magnetic field (e.g. moving permanent magnet) causes

More information

Chapter 31. Faraday s Law

Chapter 31. Faraday s Law Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field dφ B ( I I ) E d s = µ o + d = µ o I+ µ oεo ds E B 2 Induction A loop of wire is connected to a sensitive

More information

Faraday s Law of Electromagnetic Induction

Faraday s Law of Electromagnetic Induction Faraday s Law of Electromagnetic Induction 2.1 Represent and reason The rectangular loop with a resistor is pulled at constant velocity through a uniform external magnetic field that points into the paper

More information

PHY 131 Review Session Fall 2015 PART 1:

PHY 131 Review Session Fall 2015 PART 1: PHY 131 Review Session Fall 2015 PART 1: 1. Consider the electric field from a point charge. As you move farther away from the point charge, the electric field decreases at a rate of 1/r 2 with r being

More information

Induced Electric Field

Induced Electric Field Lecture 18 Chapter 33 Physics II Induced Electric Field Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Applications of Faraday s Law (some leftovers from the previous class) Applications

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 2140) Lecture 15 Electricity and Magnetism Magnetism Applications of magnetic forces Induced voltages and induction Magnetic flux and induced emf Faraday s law http://www.physics.wayne.edu/~apetrov/phy2140/

More information

Lecture 24. April 5 th, Magnetic Circuits & Inductance

Lecture 24. April 5 th, Magnetic Circuits & Inductance Lecture 24 April 5 th, 2005 Magnetic Circuits & Inductance Reading: Boylestad s Circuit Analysis, 3 rd Canadian Edition Chapter 11.1-11.5, Pages 331-338 Chapter 12.1-12.4, Pages 341-349 Chapter 12.7-12.9,

More information

Chapter 9 FARADAY'S LAW Recommended Problems:

Chapter 9 FARADAY'S LAW Recommended Problems: Chapter 9 FARADAY'S LAW Recommended Problems: 5,7,9,10,11,13,15,17,20,21,28,29,31,32,33,34,49,50,52,58,63,64. Faraday's Law of Induction We learned that e. current produces magnetic field. Now we want

More information

Chapter 32. Inductance

Chapter 32. Inductance Chapter 32 Inductance Joseph Henry 1797 1878 American physicist First director of the Smithsonian Improved design of electromagnet Constructed one of the first motors Discovered self-inductance Unit of

More information

AAST/AEDT. Electromagnetic Induction. If the permanent magnet is at rest, then - there is no current in a coil.

AAST/AEDT. Electromagnetic Induction. If the permanent magnet is at rest, then - there is no current in a coil. 1 AP PHYSICS C AAST/AEDT Electromagnetic Induction Let us run several experiments. 1. A coil with wire is connected with the Galvanometer. If the permanent magnet is at rest, then - there is no current

More information

r where the electric constant

r where the electric constant 1.0 ELECTROSTATICS At the end of this topic, students will be able to: 10 1.1 Coulomb s law a) Explain the concepts of electrons, protons, charged objects, charged up, gaining charge, losing charge, charging

More information

PHYS 272 (Spring 2018): Introductory Physics: Fields Problem-solving sessions

PHYS 272 (Spring 2018): Introductory Physics: Fields Problem-solving sessions Figure 1: Problem 1 Figure 2: Problem 2 PHYS 272 (Spring 2018): Introductory Physics: Fields Problem-solving sessions (1). A thin rod of length l carries a total charge Q distributed uniformly along its

More information

Tactics: Evaluating line integrals

Tactics: Evaluating line integrals Tactics: Evaluating line integrals Ampère s law Whenever total current I through passes through an area bounded by a closed curve, the line integral of the magnetic field around the curve is given by Ampère

More information

Physics 102: Lecture 10. Faraday s Law. Changing Magnetic Fields create Electric Fields. Physics 102: Lecture 10, Slide 1

Physics 102: Lecture 10. Faraday s Law. Changing Magnetic Fields create Electric Fields. Physics 102: Lecture 10, Slide 1 Physics 102: Lecture 10 Faraday s Law Changing Magnetic Fields create Electric Fields Physics 102: Lecture 10, Slide 1 Last Two Lectures Magnetic fields Forces on moing charges and currents Torques on

More information

Lecture 13.2 :! Inductors

Lecture 13.2 :! Inductors Lecture 13.2 :! Inductors Lecture Outline:! Induced Fields! Inductors! LC Circuits! LR Circuits!! Textbook Reading:! Ch. 33.6-33.10 April 9, 2015 1 Announcements! HW #10 due on Tuesday, April 14, at 9am.!

More information

Slide 1 / 26. Inductance by Bryan Pflueger

Slide 1 / 26. Inductance 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

Lecture 30: WED 04 NOV

Lecture 30: WED 04 NOV Physics 2113 Jonathan Dowling Lecture 30: WED 04 NOV Induction and Inductance II Fender Stratocaster Solenoid Pickup F a r a d a y ' s E x p e r i m e n t s I n a s e r i e s o f e x p e r i m e n t s,

More information

Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the time-varying current.

Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the time-varying current. Inductance Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the time-varying current. Basis of the electrical circuit element called an

More information

Lecture 27: FRI 20 MAR

Lecture 27: FRI 20 MAR Physics 2102 Jonathan Dowling Lecture 27: FRI 20 MAR Ch.30.7 9 Inductors & Inductance Nikolai Tesla Inductors: Solenoids Inductors are with respect to the magnetic field what capacitors are with respect

More information

Lecture 13.1 :! Electromagnetic Induction Continued

Lecture 13.1 :! Electromagnetic Induction Continued Lecture 13.1 :! Electromagnetic Induction Continued Lecture Outline:! Faraday s Law! Induced Fields! Applications! Textbook Reading:! Ch. 33.5-33.7 April 7, 2015 1 Announcements! Homework #10 due on Tuesday,

More information

Electromagnetic Induction! March 11, 2014 Chapter 29 1

Electromagnetic Induction! March 11, 2014 Chapter 29 1 Electromagnetic Induction! March 11, 2014 Chapter 29 1 Notes! Exam 4 next Tuesday Covers Chapters 27, 28, 29 in the book Magnetism, Magnetic Fields, Electromagnetic Induction Material from the week before

More information

PHY101: Major Concepts in Physics I

PHY101: Major Concepts in Physics I Welcome back to PHY101: Major Concepts in Physics I Photo: J. M. Schwarz Announcements In class today we will finish Chapter 20 (sections 3, 4, and 7). and then move to Chapter 13 (the first six sections).

More information

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1 Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/1 Magnetic flux What is a magnetic flux? This is very similar to the concept of an electric flux through an area

More information

Exam 2 Solutions. Answer: 3.0 W Solution: The total current is in the series circuit is 1 A, so the power dissipated in R 2 is i 2 R 2

Exam 2 Solutions. Answer: 3.0 W Solution: The total current is in the series circuit is 1 A, so the power dissipated in R 2 is i 2 R 2 Exam 2 Solutions Prof. Pradeep Kumar Prof. Paul Avery Mar. 21, 2012 1. A portable CD player does not have a power rating listed, but it has a label stating that it draws a maximum current of 159.0 ma.

More information