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

Size: px
Start display at page:

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

Transcription

1 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 inductor Energy is stored in the magnetic field of an inductor. There is an energy density associated with the magnetic field. Mutual induction An emf is induced in a coil as a result of a changing magnetic flux produced by a second coil. Circuits may contain inductors as well as resistors and capacitors. Introduction

2 Joseph Henry American physicist First director of the Smithsonian First president of the Academy of Natural Science Improved design of electromagnet Constructed one of the first motors Discovered self-inductance Didn t publish his results Unit of inductance is named in his honor Section 32.1

3 Some Terminology Use emf and current when they are caused by batteries or other sources. Use induced emf and induced current when they are caused by changing magnetic fields. When dealing with problems in electromagnetism, it is important to distinguish between the two situations. Section 32.1

4 Self-Inductance When the switch is closed, the current does not immediately reach its maximum value. Faraday s law of electromagnetic induction can be used to describe the effect. As the current increases with time, the magnetic flux through the circuit loop due to this current also increases with time. This increasing flux creates an induced emf in the circuit. Section 32.1

5 RL Circuit, Current-Time Graph, Charging The equilibrium value of the current is e /R and is reached as t approaches infinity. The current initially increases very rapidly. The current then gradually approaches the equilibrium value. Section 32.2

6 RL Circuit, Current-Time Graph, Discharging The time rate of change of the current is a maximum at t = 0. It falls off exponentially as t approaches infinity. In general, di dt ε e L t τ Section 32.2

7 EXAMPLE Large voltage across an inductor

8 EXAMPLE An AM radio oscillator QUESTION:

9 Rank in order, from largest to smallest, the time constants τ a, τ b, and τ c of these three circuits. A. τ a > τ b > τ c B. τ b > τ a > τ c C. τ b > τ c > τ a D. τ c > τ a > τ b E. τ c > τ b > τ a

10 Rank in order, from largest to smallest, the time constants τ a, τ b, and τ c of these three circuits. A. τ a > τ b > τ c B. τ b > τ a > τ c C. τ b > τ c > τ a D. τ c > τ a > τ b E. τ c > τ b > τ a

11 LC Circuits A capacitor is connected to an inductor in an LC circuit. Assume the capacitor is initially charged and then the switch is closed. Assume no resistance and no energy losses to radiation. Section 32.5

12 Oscillations in an LC Circuit Under the previous conditions, the current in the circuit and the charge on the capacitor oscillate between maximum positive and negative values. With zero resistance, no energy is transformed into internal energy. Ideally, the oscillations in the circuit persist indefinitely. The idealizations are no resistance and no radiation. The capacitor is fully charged. The energy U in the circuit is stored in the electric field of the capacitor. The energy is equal to Q 2 max / 2C. The current in the circuit is zero. No energy is stored in the inductor. The switch is closed. Section 32.5

13 Oscillations in an LC Circuit, cont. The current is equal to the rate at which the charge changes on the capacitor. As the capacitor discharges, the energy stored in the electric field decreases. Since there is now a current, some energy is stored in the magnetic field of the inductor. Energy is transferred from the electric field to the magnetic field. Eventually, the capacitor becomes fully discharged. It stores no energy. All of the energy is stored in the magnetic field of the inductor. The current reaches its maximum value. The current now decreases in magnitude, recharging the capacitor with its plates having opposite their initial polarity. Section 32.5

14 Oscillations in an LC Circuit, final The capacitor becomes fully charged and the cycle repeats. The energy continues to oscillate between the inductor and the capacitor. The total energy stored in the LC circuit remains constant in time and equals. 2 Q 1 U U 2 2 I C UL L C 2 Section 32.5

15 LC Circuit Analogy to Spring-Mass System, 1 The potential energy ½kx 2 stored in the spring is analogous to the electric potential energy (Q max ) 2 /(2C) stored in the capacitor. All the energy is stored in the capacitor at t = 0. This is analogous to the spring stretched to its amplitude. Section 32.5

16 LC Circuit Analogy to Spring-Mass System, 2 The kinetic energy (½ mv 2 ) of the spring is analogous to the magnetic energy (½ L I 2 ) stored in the inductor. At t = ¼ T, all the energy is stored as magnetic energy in the inductor. The maximum current occurs in the circuit. This is analogous to the mass at equilibrium. Section 32.5

17 LC Circuit Analogy to Spring-Mass System, 3 At t = ½ T, the energy in the circuit is completely stored in the capacitor. The polarity of the capacitor is reversed. This is analogous to the spring stretched to -A. Section 32.5

18 LC Circuit Analogy to Spring-Mass System, 4 At t = ¾ T, the energy is again stored in the magnetic field of the inductor. This is analogous to the mass again reaching the equilibrium position. Section 32.5

19 LC Circuit Analogy to Spring-Mass System, 5 At t = T, the cycle is completed The conditions return to those identical to the initial conditions. At other points in the cycle, energy is shared between the electric and magnetic fields. Section 32.5

20 Time Functions of an LC Circuit In an LC circuit, charge can be expressed as a function of time. Q = Q max cos (ωt + φ) This is for an ideal LC circuit The angular frequency, ω, of the circuit depends on the inductance and the capacitance. It is the natural frequency of oscillation of the circuit. ω 1 LC Section 32.5

21 Time Functions of an LC Circuit, cont. The current can be expressed as a function of time: dq I ωqmax sin(ωt φ) dt The total energy can be expressed as a function of time: 2 Qmax U UC UL cos ωt LImax sin ωt 2c 2 Section 32.5

22 Charge and Current in an LC Circuit The charge on the capacitor oscillates between Q max and -Q max. The current in the inductor oscillates between I max and -I max. Q and I are 90 o out of phase with each other So when Q is a maximum, I is zero, etc. ω 1 LC Section 32.5

23 Energy in an LC Circuit Graphs The energy continually oscillates between the energy stored in the electric and magnetic fields. When the total energy is stored in one field, the energy stored in the other field is zero. 2 Qmax U UC UL cos ωt LImax sin ωt 2c 2 ω 1 LC Section 32.5

24 Notes About Real LC Circuits In actual circuits, there is always some resistance. Therefore, there is some energy transformed to internal energy. Radiation is also inevitable in this type of circuit. The total energy in the circuit continuously decreases as a result of these processes. Section 32.5

25 The RLC Circuit A circuit containing a resistor, an inductor and a capacitor is called an RLC Circuit. Assume the resistor represents the total resistance of the circuit. Section 32.6

26 RLC Circuit, Analysis The total energy is not constant, since there is a transformation to internal energy in the resistor at the rate of du/dt = -I 2 R. Radiation losses are still ignored The circuit s operation can be expressed as 2 L d Q R dq Q 0 2 dt dt C Section 32.6

27 RLC Circuit Compared to Damped Oscillators The RLC circuit is analogous to a damped harmonic oscillator. When R = 0 The circuit reduces to an LC circuit and is equivalent to no damping in a mechanical oscillator. When R is small: The RLC circuit is analogous to light damping in a mechanical oscillator. Q = Q max e -Rt/2L cos ω d t ω d is the angular frequency of oscillation for the circuit and ω d 1 LC R 2L Section 32.6

28 RLC Circuit Compared to Damped Oscillators, cont. When R is very large, the oscillations damp out very rapidly. There is a critical value of R above which no oscillations occur. RC 4 L / C If R = R C, the circuit is said to be critically damped. When R > R C, the circuit is said to be overdamped. Section 32.6

29 Damped RLC Circuit, Graph The maximum value of Q decreases after each oscillation. R < R C This is analogous to the amplitude of a damped spring-mass system. Section 32.6

30 Summary: Analogies Between Electrical and Mechanic Systems Section 32.6

31

32

33

34 Problem-Solving Strategy: Electromagnetic Induction

35 Self-Inductance, cont. The direction of the induced emf is such that it would cause an induced current in the loop which would establish a magnetic field opposing the change in the original magnetic field. The direction of the induced emf is opposite the direction of the emf of the battery. This results in a gradual increase in the current to its final equilibrium value. This effect is called self-inductance. Because the changing flux through the circuit and the resultant induced emf arise from the circuit itself. The emf ε L is called a self-induced emf. Section 32.1

36 Self-Inductance, Equations An induced emf is always proportional to the time rate of change of the current. The emf is proportional to the flux, which is proportional to the field and the field is proportional to the current. ε L di L dt L is a constant of proportionality called the inductance of the coil. It depends on the geometry of the coil and other physical characteristics. Section 32.1

37 Inductance of a Coil A closely spaced coil of N turns carrying current I has an inductance of L N I B εl d I dt The inductance is a measure of the opposition to a change in current. Section 32.1

38 Inductance Units The SI unit of inductance is the henry (H) V s 1H 1 A Named for Joseph Henry Section 32.1

39 Inductance of a Solenoid Assume a uniformly wound solenoid having N turns and length l. Assume l is much greater than the radius of the solenoid. The flux through each turn of area A is N BA μ ni A μ I A B o o The inductance is L 2 N B μon A I 2 μon V This shows that L depends on the geometry of the object. Section 32.1

40 RL Circuit, Introduction A circuit element that has a large self-inductance is called an inductor. The circuit symbol is We assume the self-inductance of the rest of the circuit is negligible compared to the inductor. However, even without a coil, a circuit will have some self-inductance. Section 32.2

41 Effect of an Inductor in a Circuit The inductance results in a back emf. Therefore, the inductor in a circuit opposes changes in current in that circuit. The inductor attempts to keep the current the same way it was before the change occurred. The inductor can cause the circuit to be sluggish as it reacts to changes in the voltage. Section 32.2

42 RL Circuit, Analysis An RL circuit contains an inductor and a resistor. Assume S 2 is connected to a When switch S 1 is closed (at time t = 0), the current begins to increase. At the same time, a back emf is induced in the inductor that opposes the original increasing current. Section 32.2

43 RL Circuit, Analysis, cont. Applying Kirchhoff s loop rule to the previous circuit in the clockwise direction gives di ε I R L dt 0 Looking at the current, we find I ε R 1 e Rt L Section 32.2

44 RL Circuit, Analysis, Final The inductor affects the current exponentially. The current does not instantly increase to its final equilibrium value. If there is no inductor, the exponential term goes to zero and the current would instantaneously reach its maximum value as expected. Section 32.2

45 RL Circuit, Time Constant The expression for the current can also be expressed in terms of the time constant, t, of the circuit. I ε R 1 e t τ where t = L / R Physically, t is the time required for the current to reach 63.2% of its maximum value. Section 32.2

46 RL Circuit Without A Battery Now set S 2 to position b The circuit now contains just the right hand loop. The battery has been eliminated. The expression for the current becomes ε t τ I e Iie R t τ Section 32.2

47 Energy in a Magnetic Field In a circuit with an inductor, the battery must supply more energy than in a circuit without an inductor. Part of the energy supplied by the battery appears as internal energy in the resistor. The remaining energy is stored in the magnetic field of the inductor. Section 32.3

48 Energy in a Magnetic Field, cont. Looking at this energy (in terms of rate) 2 di I ε I R LI dt Ie is the rate at which energy is being supplied by the battery. I 2 R is the rate at which the energy is being delivered to the resistor. Therefore, LI (di/dt) must be the rate at which the energy is being stored in the magnetic field. Section 32.3

49 Energy in a Magnetic Field, final Let U denote the energy stored in the inductor at any time. The rate at which the energy is stored is du d I LI dt dt To find the total energy, integrate and I 1 U L I d I LI Section 32.3

50 Energy Density of a Magnetic Field Given U = ½ L I 2 and assume (for simplicity) a solenoid with L = m o n 2 V B B U μon V V 2 μon 2μo Since V is the volume of the solenoid, the magnetic energy density, u B is u B U V B 2μ 2 o This applies to any region in which a magnetic field exists (not just the solenoid). Section 32.3

51 Energy Storage Summary A resistor, inductor and capacitor all store energy through different mechanisms. Charged capacitor Stores energy as electric potential energy Inductor When it carries a current, stores energy as magnetic potential energy Resistor Energy delivered is transformed into internal energy Section 32.3

52 Example: The Coaxial Cable Calculate L of a length l for the cable The total flux is b μo I B B da a 2πr μo I b ln 2π a dr Therefore, L is L B μo b ln I 2π a Section 32.3

53 Mutual Inductance The magnetic flux through the area enclosed by a circuit often varies with time because of time-varying currents in nearby circuits. This process is known as mutual induction because it depends on the interaction of two circuits. Section 32.4

54 Mutual Inductance, cont. The current in coil 1 sets up a magnetic field. Some of the magnetic field lines pass through coil 2. Coil 1 has a current I 1 and N 1 turns. Coil 2 has N 2 turns. Section 32.4

55 Mutual Inductance, final The mutual inductance M 12 of coil 2 with respect to coil 1 is M 12 N I Mutual inductance depends on the geometry of both circuits and on their orientation with respect to each other. Section 32.4

56 Induced emf in Mutual Inductance If current I 1 varies with time, the emf induced by coil 1 in coil 2 is d ε N M dt d I dt If the current is in coil 2, there is a mutual inductance M 21. If current 2 varies with time, the emf induced by coil 2 in coil 1 is di 2 ε1 M21 dt Section 32.4

57 Induced emf in Mutual Inductance, cont. In mutual induction, the emf induced in one coil is always proportional to the rate at which the current in the other coil is changing. The mutual inductance in one coil is equal to the mutual inductance in the other coil. M 12 = M 21 = M The induced emf s can be expressed as d I d I ε M and ε M dt dt Section 32.4

### 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

### Chapter 32. Inductance

Chapter 32 Inductance 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

### Active Figure 32.3 (SLIDESHOW MODE ONLY)

RL Circuit, Analysis An RL circuit contains an inductor and a resistor When the switch is closed (at time t = 0), the current begins to increase At the same time, a back emf is induced in the inductor

### 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

### Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits

Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying

### 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

### 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

### Chapter 31. Faraday s Law

Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field B s II I d d μ o d μo με o o E ds E B Induction A loop of wire is connected to a sensitive ammeter

### Chapter 30 Inductance and Electromagnetic Oscillations

Chapter 30 Inductance and Electromagnetic Oscillations Units of Chapter 30 30.1 Mutual Inductance: 1 30.2 Self-Inductance: 2, 3, & 4 30.3 Energy Stored in a Magnetic Field: 5, 6, & 7 30.4 LR Circuit: 8,

### 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

### 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

### Inductance. Chapter Outline Self-Inductance 32.2 RL Circuits 32.3 Energy in a Magnetic Field

P U Z Z L E R The marks in the pavement are part of a sensor that controls the traffic lights at this intersection. What are these marks, and how do they detect when a car is waiting at the light? ( David

### 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

### Inductance, RL Circuits, LC Circuits, RLC Circuits

Inductance, R Circuits, C Circuits, RC Circuits Inductance What happens when we close the switch? The current flows What does the current look like as a function of time? Does it look like this? I t Inductance

### Chapter 32. nductance

Chapter 32 nductance C HAP T E R O UT N E 321 elf-nductance 322 R Circuits 323 Energy in a Magnetic Field 324 Mutual nductance 325 Oscillations in an Circuit 326 The R Circuit An airport metal detector

### 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

### Chapter 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 self-inductance. An inductor is formed by taken

### 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

### Inductance. Slide 2 / 26. Slide 1 / 26. Slide 4 / 26. Slide 3 / 26. Slide 6 / 26. Slide 5 / 26. Mutual Inductance. Mutual Inductance.

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

### 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

### 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

### Electromagnetic Oscillations and Alternating Current. 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3.

Electromagnetic Oscillations and Alternating Current 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3. RLC circuit in AC 1 RL and RC circuits RL RC Charging Discharging I = emf R

### Chapter 30. Inductance. PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow

Chapter 30 Inductance PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Learning Goals for Chapter 30 Looking forward at how a time-varying

### 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

### Lecture 39. PHYC 161 Fall 2016

Lecture 39 PHYC 161 Fall 016 Announcements DO THE ONLINE COURSE EVALUATIONS - response so far is < 8 % Magnetic field energy A resistor is a device in which energy is irrecoverably dissipated. By contrast,

### Chapter 30 Examples : Inductance (sections 1 through 6) Key concepts: (See chapter 29 also.)

Chapter 30 Examples : Inductance (sections 1 through 6) Key concepts: (See chapter 29 also.) ξ 2 = MdI 1 /dt : A changing current in a coil of wire (1) will induce an EMF in a second coil (2) placed nearby.

### PHYS 1441 Section 001 Lecture #23 Monday, Dec. 4, 2017

PHYS 1441 Section 1 Lecture #3 Monday, Dec. 4, 17 Chapter 3: Inductance Mutual and Self Inductance Energy Stored in Magnetic Field Alternating Current and AC Circuits AC Circuit W/ LRC Chapter 31: Maxwell

### Chapter 30 INDUCTANCE. Copyright 2012 Pearson Education Inc.

Chapter 30 INDUCTANCE Goals for Chapter 30 To learn how current in one coil can induce an emf in another unconnected coil To relate the induced emf to the rate of change of the current To calculate the

### 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

### 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

### 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

### Chapter 14 Inductance 627

Chapter 14 Inductance 627 14 INDUCTANCE Figure 14.1 A smartphone charging mat contains a coil that receives alternating current, or current that is constantly increasing and decreasing. The varying current

### 11 Chapter. Inductance and Magnetic Energy

11 Chapter Inductance and Magnetic Energy 11.1 Mutual Inductance... 11-3 Example 11.1 Mutual Inductance of Two Concentric Co-planar Loops... 11-5 11.2 Self-Inductance... 11-6 Example 11.2 Self-Inductance

### 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

### PHYS 241 EXAM #2 November 9, 2006

1. ( 5 points) A resistance R and a 3.9 H inductance are in series across a 60 Hz AC voltage. The voltage across the resistor is 23 V and the voltage across the inductor is 35 V. Assume that all voltages

### Module 22 and 23: Section 11.1 through Section 11.4 Module 24: Section 11.4 through Section Table of Contents

Module and 3: Section 11.1 through Section 11.4 Module 4: Section 11.4 through Section 11.13 1 Table of Contents Inductance and Magnetic Energy... 11-3 11.1 Mutual Inductance... 11-3 Example 11.1 Mutual

### RLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is

RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge

### Yell if you have any questions

Class 31: Outline Hour 1: Concept Review / Overview PRS Questions possible exam questions Hour : Sample Exam Yell if you have any questions P31 1 Exam 3 Topics Faraday s Law Self Inductance Energy Stored

### 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

### Assessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526)

NCEA Level 3 Physics (91526) 2015 page 1 of 6 Assessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526) Evidence Q Evidence Achievement Achievement with Merit Achievement

### Physics for Scientists & Engineers 2

Electromagnetic Oscillations Physics for Scientists & Engineers Spring Semester 005 Lecture 8! We have been working with circuits that have a constant current a current that increases to a constant current

### 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

### PES 1120 Spring 2014, Spendier Lecture 35/Page 1

PES 0 Spring 04, Spendier Lecture 35/Page Today: chapter 3 - LC circuits We have explored the basic physics of electric and magnetic fields and how energy can be stored in capacitors and inductors. We

### 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,

### 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

### Lecture Sound Waves Review. Physics Help Q&A: tutor.leiacademy.org. Force on a Charge Moving in a Magnetic Field

Lecture 1101 Sound Waves Review Physics Help Q&A: tutor.leiacademy.org Force on a Charge Moving in a Magnetic Field A charge moving in a magnetic field can have a magnetic force exerted by the B-field.

### EM Oscillations. David J. Starling Penn State Hazleton PHYS 212

I ve got an oscillating fan at my house. The fan goes back and forth. It looks like the fan is saying No. So I like to ask it questions that a fan would say no to. Do you keep my hair in place? Do you

### Magnets. Domain = small magnetized region of a magnetic material. all the atoms are grouped together and aligned

Magnetic Fields Magnets Domain = small magnetized region of a magnetic material all the atoms are grouped together and aligned Magnets Ferromagnetic materials domains can be forced to line up by applying

### Chapter 21 Magnetic Induction Lecture 12

Chapter 21 Magnetic Induction Lecture 12 21.1 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

### 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.

### 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

### Physics 2020 Exam 2 Constants and Formulae

Physics 2020 Exam 2 Constants and Formulae Useful Constants k e = 8.99 10 9 N m 2 /C 2 c = 3.00 10 8 m/s ɛ = 8.85 10 12 C 2 /(N m 2 ) µ = 4π 10 7 T m/a e = 1.602 10 19 C h = 6.626 10 34 J s m p = 1.67

### Chapter 30 Self Inductance, Inductors & DC Circuits Revisited

Chapter 30 Self Inductance, Inductors & DC Circuits Revisited Self-Inductance and Inductors Self inductance determines the magnetic flux in a circuit due to the circuit s own current. B = LI Every circuit

### Exam 3 Topics. Displacement Current Poynting Vector. Faraday s Law Self Inductance. Circuits. Energy Stored in Inductor/Magnetic Field

Exam 3 Topics Faraday s Law Self Inductance Energy Stored in Inductor/Magnetic Field Circuits LR Circuits Undriven (R)LC Circuits Driven RLC Circuits Displacement Current Poynting Vector NO: B Materials,

### 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

### Exam 3 Solutions. The induced EMF (magnitude) is given by Faraday s Law d dt dt The current is given by

PHY049 Spring 008 Prof. Darin Acosta Prof. Selman Hershfield April 9, 008. A metal rod is forced to move with constant velocity of 60 cm/s [or 90 cm/s] along two parallel metal rails, which are connected

### Magnetic Induction Faraday, Lenz, Mutual & Self Inductance Maxwell s Eqns, E-M waves. Reading Journals for Tuesday from table(s)

PHYS 2015 -- Week 12 Magnetic Induction Faraday, Lenz, Mutual & Self Inductance Maxwell s Eqns, E-M waves Reading Journals for Tuesday from table(s) WebAssign due Friday night For exclusive use in PHYS

### Lecture 22. Inductance. Magnetic Field Energy.

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.

### University of California, Berkeley Physics H7B Spring 1999 (Strovink) SOLUTION TO PROBLEM SET 11 Solutions by P. Pebler

University of California Berkeley Physics H7B Spring 999 (Strovink) SOLUTION TO PROBLEM SET Solutions by P. Pebler Purcell 7.2 A solenoid of radius a and length b is located inside a longer solenoid of

### Self-Inductance. Φ i. Self-induction. = (if flux Φ 1 through 1 loop. Tm Vs A A. Lecture 11-1

Lecture - Self-Inductance As current i through coil increases, magnetic flux through itself increases. This in turn induces back emf in the coil itself When current i is decreasing, emf is induced again

### Exam 2 Solutions. Note that there are several variations of some problems, indicated by choices in parentheses.

Exam 2 Solutions Note that there are several variations of some problems, indicated by choices in parentheses. Problem 1 Part of a long, straight insulated wire carrying current i is bent into a circular

### Louisiana State University Physics 2102, Exam 3 April 2nd, 2009.

PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),

### 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

### Chapter 28. Direct Current Circuits

Chapter 28 Direct Current Circuits Circuit Analysis Simple electric circuits may contain batteries, resistors, and capacitors in various combinations. For some circuits, analysis may consist of combining

### 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

### 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

### Electrical polarization. Figure 19-5 [1]

Electrical polarization Figure 19-5 [1] Properties of Charge Two types: positive and negative Like charges repel, opposite charges attract Charge is conserved Fundamental particles with charge: electron

### ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT

Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the

### 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.

### Alternating Current Circuits. Home Work Solutions

Chapter 21 Alternating Current Circuits. Home Work s 21.1 Problem 21.11 What is the time constant of the circuit in Figure (21.19). 10 Ω 10 Ω 5.0 Ω 2.0µF 2.0µF 2.0µF 3.0µF Figure 21.19: Given: The circuit

### 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

### 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

### 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

### Louisiana State University Physics 2102, Exam 3, November 11, 2010.

Name: Instructor: Louisiana State University Physics 2102, Exam 3, November 11, 2010. Please be sure to write your name and class instructor above. The test consists of 3 questions (multiple choice), and

### 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

### Lecture 22. Inductance. Magnetic Field Energy.

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.

### Chapter 32 Solutions

Chapter 3 Solutions *3. ε = L I t = (3.00 0 3 H).50 A 0.00 A 0.00 s =.95 0 V = 9.5 mv 3. Treating the telephone cord as a solenoid, we have: L = µ 0 N A l = (4π 0 7 T m/a)(70.0) (π)(6.50 0 3 m) 0.600 m

### Chapter 31: RLC Circuits. PHY2049: Chapter 31 1

hapter 31: RL ircuits PHY049: hapter 31 1 L Oscillations onservation of energy Topics Damped oscillations in RL circuits Energy loss A current RMS quantities Forced oscillations Resistance, reactance,

### Electromagnetic Induction and Waves (Chapters 33-34)

Electromagnetic nduction and Waves (Chapters 33-34) The laws of emf induction: Faraday s and Lenz s laws Concepts of classical electromagnetism. Maxwell equations nductance Mutual inductance M Self inductance

### ε induced Review: Self-inductance 20.7 RL Circuits Review: Self-inductance B induced Announcements

Announcements WebAssign HW Set 7 due this Friday Problems cover material from Chapters 20 and 21 We re skipping Sections 21.1-21.7 (alternating current circuits) Review: Self-inductance induced ε induced

### AP Physics C. Inductance. Free Response Problems

AP Physics C Inductance Free Response Problems 1. Two toroidal solenoids are wounded around the same frame. Solenoid 1 has 800 turns and solenoid 2 has 500 turns. When the current 7.23 A flows through

### Physics Notes for Class 12 chapter 6 ELECTROMAGNETIC I NDUCTION

1 P a g e Physics Notes for Class 12 chapter 6 ELECTROMAGNETIC I NDUCTION Whenever the magnetic flux linked with an electric circuit changes, an emf is induced in the circuit. This phenomenon is called

### 1 2 U CV. K dq I dt J nqv d J V IR P VI

o 5 o T C T F 3 9 T K T o C 73.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC L pv nrt 3 Ktr nrt 3 CV R ideal monatomic gas 5 CV R ideal diatomic gas w/o vibration V W pdv V U Q W W Q e Q Q e Carnot

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2003 Experiment 17: RLC Circuit (modified 4/15/2003) OBJECTIVES

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8. Spring 3 Experiment 7: R Circuit (modified 4/5/3) OBJECTIVES. To observe electrical oscillations, measure their frequencies, and verify energy

### Assessment Schedule 2016 Physics: Demonstrate understanding electrical systems (91526)

NCEA evel 3 Physics (91526) 2016 page 1 of 5 Assessment Schedule 2016 Physics: Demonstrate understanding electrical systems (91526) Evidence Statement NØ N1 N 2 A 3 A 4 M 5 M 6 E 7 E 8 0 1A 2A 3A 4A or

### The self-inductance depends on the geometric shape of the coil. An inductor is a coil of wire used in a circuit to provide inductance is an inductor.

Self Inductance and Mutual Inductance Script Self-Inductance Consider a coil carrying a current i. The current in the coil produces a magnetic field B that varies from point to point in the coil. The magnetic

### David J. Starling Penn State Hazleton PHYS 212

and and The term inductance was coined by Oliver Heaviside in February 1886. David J. Starling Penn State Hazleton PHYS 212 and We have seen electric flux: Φ E = E d A But we can define the magnetic flux

### Electricity and Magnetism Energy of the Magnetic Field Mutual Inductance

Electricity and Magnetism Energy of the Magnetic Field Mutual Inductance Lana Sheridan De Anza College Mar 14, 2018 Last time inductors resistor-inductor circuits Overview wrap up resistor-inductor circuits

### Module 24: Outline. Expt. 8: Part 2:Undriven RLC Circuits

Module 24: Undriven RLC Circuits 1 Module 24: Outline Undriven RLC Circuits Expt. 8: Part 2:Undriven RLC Circuits 2 Circuits that Oscillate (LRC) 3 Mass on a Spring: Simple Harmonic Motion (Demonstration)

### Inductive & Capacitive Circuits. Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur

Inductive & Capacitive Circuits Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur LR Circuit LR Circuit (Charging) Let us consider a circuit having an inductance

### Alternating Current. Symbol for A.C. source. A.C.

Alternating Current Kirchoff s rules for loops and junctions may be used to analyze complicated circuits such as the one below, powered by an alternating current (A.C.) source. But the analysis can quickly

### Yell if you have any questions

Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 efore Starting All of your grades should now be posted

### 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

### Physics 420 Fall 2004 Quiz 1 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers.

Quiz 1 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. A charge q 1 = +5.0 nc is located on the y-axis, 15 µm above the origin, while another charge q

### Induced e.m.f. on solenoid itself

Induced e.m.f. Consider a loop of wire with radius r inside a long enoid Solenoid: N# of loops, ltotal length nn/l I I (t) What is the e.m.f. generated in the loop? Find inside enoid: E.m.f. generated

### 2.4 Models of Oscillation

2.4 Models of Oscillation In this section we give three examples of oscillating physical systems that can be modeled by the harmonic oscillator equation. Such models are ubiquitous in physics, but are