Lecture 24. April 5 th, Magnetic Circuits & Inductance
|
|
- Sabina Armstrong
- 5 years ago
- Views:
Transcription
1 Lecture 24 April 5 th, 2005 Magnetic Circuits & Inductance Reading: Boylestad s Circuit Analysis, 3 rd Canadian Edition Chapter , Pages Chapter , Pages Chapter , Pages Note: We do NOT cover RL Transients (12.5-6) Assignment: Assignment #11 Due: N/A
2 Magnetic Circuits & Inductance Electric Circuit Magnetic Circuit Name Equation Units Units Equation Name Electric Current A Wb Magnetic Flux Electromotive Force (emf) Resistance V I = R I Φ = R = V V At I NI Magneto-motive force (mmf) Ω At/Wb Reluctance R = ρ l A l R = µ A Permittivity ε 0 F/m Wb/Atm µ 0 Permeability Capacitance C Farads Henries L Inductance τ RC seconds seconds R/L τ Electric flux density D Ψ WB/m 2 Φ Magnetic Flux density = Β = A A Electric Field V V/m At/m Intensity E = H = I Magnetic Field Intensity d l Aside: The following 3 constants are exact: Permittivity of free space: ε 0 = x F/m Permeability of free space: µ 0 = 4π x 10-7 H/m Speed of light: c = m/s Now ε 0 µ 0 =1/c 2 Coincidence??? April 5 th, 2005 Magnetic Circuits & Inductance 2
3 Magnetic Circuits & Inductance: In what follows a new circuit element for use in E.P is going to be introduced. It is called an inductor. You will notice during the development that inductance is in some ways similar to previous circuit elements while at the same time having some unusual characteristics! Magnetic circuit analysis is difficult and many assumptions are made. Magnetism: You probably have noticed at some point in your life that opposite poles of magnets attract (and that similar poles of magnets repel). This implies that there exists a magnetic field, analogous to an electric field, responsible for the force. April 5 th, 2005 Magnetic Circuits & Inductance 3
4 It is noted that magnetic field lines always go from the north pole of a magnet to the south pole of the magnet. Unlike electric field lines, which start on one charge and terminate on another charge, they do not start and end on each pole but are closed loops. Some materials, called ferromagnetic materials, have natural magnetic properties; the classic example is iron. They can affect neighbouring magnetic fields by capturing the magnetic field and causing it to bend. Of course there are other materials, such as plastic, that possess no magnetic properties and have no effect on the magnetic field lines. April 5 th, 2005 Magnetic Circuits & Inductance 4
5 Electromagnetism: It was noticed in past history that moving charge generates a magnetic field and therefore currents generate a magnetic field. This is the concept that electric motors operate on. The input electrical energy generates a current that creates a magnetic field that interacts with permanent magnets to turn the motor. The Permanent Magnet Moving Coil (PMMC) discussed as part of your E.P meter lectures works on this concept (although on a much smaller scale than an electric motor). The magnetic field strength is given the symbol B and has units of Teslas (T). B is also called the magnetic flux density (recall the previous information on electric flux density). Thus 1 Tesla = (1 Weber/m 2 ) = (1 Wb/m 2 ). Like the electric field E, the B field is a vector field so at all points in space it has a magnitude and direction. Unlike the electric field which is set up due to stationary charge, the magnetic field is set up due to moving charge. April 5 th, 2005 Magnetic Circuits & Inductance 5
6 Current Carrying Wire: Consider a current carrying wire (current is moving charge). p r I At point p, a perpendicular distance r from a long current carrying wire, the magnetic field strength (magnetic flux density) is µ I B = 2πr where µ is the permeability of the medium between the wire and the point p, and I is the current in the wire. Note that while we would like µ to be constant is it not, especially when we talk about ferromagnetic materials (in part due to an effect called saturation). In the examples and problems that are given as part of E.P , the µ values used for the various materials were obtained from the Normal Magnetization Curves (I & II) on Page 37. April 5 th, 2005 Magnetic Circuits & Inductance 6
7 Example #1: A long straight conductor carries a current of 100A. At what distance from the conductor is the magnetic field caused by the current equal in magnitude to the earth s magnetic field in Saskatoon (about 0.5 x 10-5 T)? April 5 th, 2005 Magnetic Circuits & Inductance 7
8 Now we have to determine the direction. This is where the concept of a magnetic field starts to diverge from that for an electric field (if it hasn t already). The direction of the magnetic field is given by the Right Hand Rule (RHR). Point your thumb of your right hand in the direction of the current and your fingers will curl in the direction of the magnetic field. In order for us to visualize this we also use arrows to help. If an arrow was coming straight at you would see the tip (designated ) while if it was going away from you would see notch end (designated ). An example diagram indicating the arrow convention is shown below. Note that the above diagram indicates something other than B (i.e., Φ). More on this very soon. April 5 th, 2005 Magnetic Circuits & Inductance 8
9 Thus for the current carrying wire you would see p r I An end view would show the following Note that the farther we move away from the wire the smaller the magnetic field strength (and magnetic flux density). April 5 th, 2005 Magnetic Circuits & Inductance 9
10 Current Loop: If we loop the wire with the current in it The direction of the magnetic field (RHR still applies) is as shown. Since B is a magnetic flux density, define Φ as the total flux with units Webers (Wb). A good way to visualize this is that the total flux is the number of magnetic field lines through a surface. B = Φ A. If the current loop is coiled to form more loops (for a total of N loops) as below What happens to the total flux? April 5 th, 2005 Magnetic Circuits & Inductance 10
11 Note that for an air coil, not all of the flux passes through all of the loops of the coil (since some of it escapes between the loops). If iron is used in the center of the coil (the core) then much more flux will pass through all of the loops since iron tends to capture the flux. The flux that passes through all of the loops is called the flux linkage. It is the flux linkage of a magnetic circuit that gives it its property of inductance. Magnetic Circuits: The flux producing ability of a coil is called its magneto-motive force (mmf). This is simply the current through the wire multiplied by the number of turns in the coil I = NI The units are Ampere-turns (At). The reluctance of a magnetic circuit is its ability to oppose the magnetic flux (this is analogous to resistance which opposes current) l R = µ A where l is the length of the magnetic circuit, A is the cross sectional area of the magnetic circuit and µ is the permeability of the core in the magnetic circuit. The units are Ampere-turns/Wb (At/Wb). Therefore I µani Φ = = R l April 5 th, 2005 Magnetic Circuits & Inductance 11
12 where Φ is the total flux generated by the magnetic circuit. There is also a Right Hand Rule (RHR) for Φ (in fact we have already seen it). If you place the fingers of your right hand along the current carrying conductors in the direction of the current in a coil, your thumb will point in the direction of the Φ. Note that permeability is analogous to permittivity. Therefore µ = µ r µ 0 where 7 µ 0 = 4π 10 Henries/m is the permeability of a vacuum (free space) and µ r is the relative permeability of the material in the core of the magnetic circuit. The relative permeability for ferromagnetic materials can be quite large (> 1000). Here is a summary of some classes of materials: Class Example Paramagnetic µ r 1 Silver, Copper Diamagnetic µ r 1 Platinum, Aluminium Ferromagnetic µ r >> 1 Iron, Nickel,AlNiCo Ferrite µ >>>> 1 Ceramics r April 5 th, 2005 Magnetic Circuits & Inductance 12
13 Magnetizing force: While the use of reluctance, R, is comfortable to use, since it looks like resistance, it turns out to be hard to use in reality. The magneto-motive force per unit length is called the magnetic field intensity and is much more commonly used H = I l and since I = NI then NI H = l. The units of H are At/m. Using some of our previous definitions it can now be shown that B = µh. The graphs shown on page 37 are examples of the variation of B with respect to H and show the non-linearity and changing value of µ for some common magnetic circuit materials. April 5 th, 2005 Magnetic Circuits & Inductance 13
14 Some Magnetic Circuits: There are two coil type magnetic circuits that we are interested in. Solenoid: Note that even with a magnetic core (like iron), the flux has to leave the core and pass through the air to get to the other end of the coil (remember the magnetic field is a continuous loop leaving one end and coming in at the other). This causes a problem. What is it??? Toroid: If we attach the ends of the solenoid to each other there is no (or very little) flux that leaves the core (especially if it is magnetic). Much more useful. April 5 th, 2005 Magnetic Circuits & Inductance 14
15 Example #2: Consider the copper core toroid with circular cross section shown below. The inside diameter is 8cm and the outside diameter is 12cm. The current through the 2000 turn coil is 1A. What is the total flux in the core? April 5 th, 2005 Magnetic Circuits & Inductance 15
16 If a conductor is moved through a magnetic field so that it cuts magnetic lines of flux, a voltage will be induced across the conductor, as shown below. The greater the number of flux lines cut per unit time (by increasing the speed with which the conductor passes through the field), or the stronger the magnetic field strength (for the same traversing speed), the greater will be the induced voltage across the conductor. If the conductor is held fixed and the magnetic field is moved so that its flux lines cut the conductor, the same effect will be produced. Faraday s Law: Voltage is induced in a magnetic circuit whenever the flux linkage is changing. The magnitude of the induced voltage is proportional to the rate of change of the flux linkages. Mathematically (note use of lower case) dφ e ind dt April 5 th, 2005 Magnetic Circuits & Inductance 16
17 where e ind is the time dependent induced voltage. As more turns are used the induced voltage is seen to increase. This leads to dφ e ind = N dt Since Φ is proportional to the current, i, through the magnetic circuit dφ dφ di e = N = N dt di dt The proportionality constant is denoted L, the self inductance of the magnetic circuit 2 di dφ di µ AN di e ind L N dt di dt l = = = dt The units of inductance are Henries. Note that Volt sec ond Volt Henry = = Ampere Ampere. second The denominator is a rate of change of current. April 5 th, 2005 Magnetic Circuits & Inductance 17
18 Lenz s Law: The polarity of the induced voltage is such that it opposes the cause of the changing flux. Therefore (from Faraday s Law) dφ e ind = N dt. The importance of this is that an inductance opposes changes in its flux. Since the flux is set up by current, the inductor opposes changes in its current (analogous to a capacitor not allowing the voltage across it to change instantaneously). April 5 th, 2005 Magnetic Circuits & Inductance 18
19 Example #3: Consider the air core solenoid shown below. What is the inductance? April 5 th, 2005 Magnetic Circuits & Inductance 19
20 Example #4: Consider the iron core solenoid shown below. The relative permeability of iron is µ r =2000µ c. What is the inductance? April 5 th, 2005 Magnetic Circuits & Inductance 20
21 So far we have looked at simple coil type magnetic circuits. In order to consider more complex circuits we need another law. Ampere s Circuital Law for Magnetic Circuits Just like there is an Ohm s Law for electric circuits there is an equivalent law for magnetic circuits, Ampere s Circuital Law. The nature of the law is essentially the same. Using the following table Electric Circuit Magnetic Circuit V I I Φ R R we can see that V can be replaced by I, I can be replaced by Φ, and R can be replaced by reluctance. We can have rises and drops around a magnetic circuit just like an electric circuit. If the elements are in series I T = I 1 + I 2 + I 3 + I 4 + R T = R 1 + R 2 + R 3 + R 4 + Note that some of the Is will be negative since the sum has to be 0 (like KVL). What about total flux (as shown below)? April 5 th, 2005 Magnetic Circuits & Inductance 21
22 Example #5: Consider the following magnetic circuit. Ampere s Circuital Law. Use I and H. Apply April 5 th, 2005 Magnetic Circuits & Inductance 22
23 Example #6: A 1000 turn coil is wound on the center leg of the magnetic circuit shown below. What is the maximum current through it if the total flux in the core must not exceed 2x10-3 Wb? The core is made of laminated sheet steel 4 cm in total thickness. The width of the outer legs is 2.5cm while the inner leg is 5 cm wide. The average path length is 25cm. Use µ sheet steel = 2.283x10-3 H/m. Hint: Symmetry may help you here. April 5 th, 2005 Magnetic Circuits & Inductance 23
24 Example #7: What is the current, I, needed to get a total flux of 2.4x10-4 Wb? µ sheet steel =1.0x10-3 H/m. April 5 th, 2005 Magnetic Circuits & Inductance 24
25 Electric Circuits with Inductors: Series inductors: Consider the following diagram. Note the presence of the resistor, R. More on R later. R L1 E L2 The current through both inductors is the same, therefore E = v L + v 1 L 2 di di E = L1 + L2 dt dt Rearranging di E = L + 1 L2. ( ) dt Thus L total = L 1 + L 2 Series inductors are similar to series resistances. April 5 th, 2005 Magnetic Circuits & Inductance 25
26 Parallel inductors: Consider the following diagram. i a R E i 1 L1 i 2 L2 Note (from KCL) i = i 1 + i 2. and v ab = vl 1 = vl 2. So di1 di2 di L1 = L2 = Ltotal dt dt dt. Noting that di di di2 = 1 + dt dt dt di vl v L2 = + = v + ab dt L1 L2 L1 L. 2 Thus L1L 2 = + L total L L or L total = L + L 1 2 b 1 2. Parallel inductances are similar to parallel resistances. April 5 th, 2005 Magnetic Circuits & Inductance 26
27 Example #8: Find the voltage V 1 and the current through each inductor. April 5 th, 2005 Magnetic Circuits & Inductance 27
28 Some interesting items: Energy stored in an inductor The energy stored in an inductor is contained within the magnetic field that is created by the current through the inductor W W W W t ( t) = 0 t ( t) = 0 t ( t) = ( t) 0 = L pdt vidt di L dt i ( t ) 0 Li W ( t) = 2 idi ( ) 2 t idt Note that there is no direct relationship to the voltage across the inductor only the current through the inductor. While a capacitor can store energy in its electric field when disconnected from a circuit, an inductor cannot store energy in its magnetic field when disconnected from a circuit (since i = 0). April 5 th, 2005 Magnetic Circuits & Inductance 28
29 Example #9: Find the energy stored in each inductor in the circuit shown below. April 5 th, 2005 Magnetic Circuits & Inductance 29
30 Voltage across an inductor: Recall that di v L = L dt. If the current through the inductor is constant di = 0 dt. Therefore is no voltage across the inductor. The significance of this is that for a circuit in which the currents are not changing (i.e., a dc circuit), no voltage exists across an inductor under steady state. As a result of this, under steady state conditions, an inductor is equivalent to a short circuit. Recall in the discussion of series and parallel inductances there was a resistor, R, in the circuit. This is to prevent the inductor(s) from shorting out the battery under steady state conditions. April 5 th, 2005 Magnetic Circuits & Inductance 30
31 What happens if current is flowing in the inductor and a switch in series with the inductor is opened? di = dt The inductor doesn t like having the current through it change. Therefore it will induce a voltage (whatever it takes) to try and keep the current flowing. This induced voltage can be quite large and will cause a breakdown of the gap between the switch contacts (switch is opening). This can cause a flashover arc. This can be quite spectacular in the dark. April 5 th, 2005 Magnetic Circuits & Inductance 31
32 Real World Effects: Note: While we discuss the following effects, in E.P we always assume (unless told otherwise) that all inductors are ideal coil inductors. Air Gaps: When an air gap in introduced into a magnetic circuit, some of the flux bulges outside of the area of the core. This is called fringing (just like in a capacitor). See diagram below. The left side shows the air gap with the bulge while the right side shows an ideal air gap. In E.P we ignore the fact that it bulges out. If we didn t, a common adjustment is to increase the length (L) and width (W) of the air gap area by the length of the air gap (l) thus creating a larger area: Area ignoring bulge: A = L x W Area with bulge: A = (L + l) x (W + l) April 5 th, 2005 Magnetic Circuits & Inductance 32
33 Laminated sheet steel cores: A large number of magnetic circuit cores are made up of laminated sheet steel cores. Laminations Varnish This is because they are cheap and they reduce the power lost through eddy currents. Eddy currents are internal currents within the steel cores due to changes in the flux and as a result of the induced voltage creating a current that circulates around the periphery of a solid core. The use of laminations reduces the power to almost negligible values. The downside to this is that the laminations have to be insulated from one another. This is done with a thin coat of varnish between the laminations. As a result, for any given area of core, the effective area has to be reduced by the total thickness of the varnish (since it is not magnetic). A common adjustment to use is a 10% reduction in area due to the varnish. April 5 th, 2005 Magnetic Circuits & Inductance 33
34 Actual inductor: Since an inductor is made up of coiled wire, it must have some resistance associated with it (due to the wire in the coil). As well, the closely spaced coils give rise to a stray capacitance between the wires of the coil. Therefore an actual inductor is modeled as below: R C 1 L The value of the resistance for a good inductor is on the order of ohms (Ω) and obviously depends on the wire size used in the coils which in turn depend on the current carrying capability of the inductor. The capacitance is usually ignored. April 5 th, 2005 Magnetic Circuits & Inductance 34
35 Variation of µ The following graphs are representative of the variation of µ with B and H. They are a) Variation of permeability with respect to H b) Hysteresis and Saturation curve c) Normal magnetization curve (I) d) Normal magnetization curve (II) We will not directly use these graphs in E.P a) Variation of permeability with respect to H From graph a) you can see that µ is anything but constant. April 5 th, 2005 Magnetic Circuits & Inductance 35
36 b) Hysteresis and Saturation curve From graph b) you can see that as H increases the B produced is non-linear and saturates near the ends. As H is then reduced there is a residual B R (top and bottom on B axis) indicating that there is a magnetic field present even if H is 0. This is the case for permanent magnets. The size of the grey area is indicative of the power lost (which causes heating) during cycling around the loop. April 5 th, 2005 Magnetic Circuits & Inductance 36
37 c) Normal Magnetisation Curve (I) Graph c) represents the initial magnetization (from o- a-b) shown in graph b). d) Normal Magnetization Curve (II) Knowing the value of B you can find the corresponding H using curve c) or d) above. This graph is an expanded version of graph c). April 5 th, 2005 Magnetic Circuits & Inductance 37
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 informationLecture Notes ELEC A6
Lecture Notes ELEC A6 Dr. Ramadan El-Shatshat Magnetic circuit 9/27/2006 Elec-A6 - Electromagnetic Energy Conversion 1 Magnetic Field Concepts Magnetic Fields: Magnetic fields are the fundamental mechanism
More informationMagnetism & Electromagnetism
Magnetism & Electromagnetism By: Dr Rosemizi Abd Rahim Click here to watch the magnetism and electromagnetism animation video http://rmz4567.blogspot.my/2013/02/electrical-engineering.html 1 Learning Outcomes
More informationEDEXCEL 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 informationMagnetic Fields
Magnetic circuits introduction Becomes aware of the similarities between the analysis of magnetic circuits and electric circuits. Develop a clear understanding of the important parameters of a magnetic
More informationMAGNETISM. Magnetism. Magnetism is a result of electrons spinning on their own axis around the nucleus (Figure 18). Basic Electrical Theory
Basic Electrical Theory Certain metals and metallic oxides have the ability to attract other metals. This property is called magnetism, and the materials which have this property are called magnets. Some
More informationThe initial magnetization curve shows the magnetic flux density that would result when an increasing magnetic field is applied to an initially
MAGNETIC CIRCUITS The study of magnetic circuits is important in the study of energy systems since the operation of key components such as transformers and rotating machines (DC machines, induction machines,
More informationChapter 1 Magnetic Circuits
Principles of Electric Machines and Power Electronics Third Edition P. C. Sen Chapter 1 Magnetic Circuits Chapter 1: Main contents i-h relation, B-H relation Magnetic circuit and analysis Property of magnetic
More informationENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 16 - INDUCTANCE
ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 16 - INDUCTANCE On completion of this tutorial you should be able to do the following. Explain inductance and inductors. Explain
More informationElectromagnetic 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 informationElectromagnetism. Topics Covered in Chapter 14:
Chapter 14 Electromagnetism Topics Covered in Chapter 14: 14-1: Ampere-turns of Magnetomotive Force (mmf) 14-2: Field Intensity (H) 14-3: B-H Magnetization Curve 14-4: Magnetic Hysteresis 14-5: Magnetic
More informationSYLLABUS(EE-205-F) SECTION-B
SYLLABUS(EE-205-F) SECTION-A MAGNETIC CIRCUITS AND INDUCTION: Magnetic Circuits, Magnetic Materials and their properties, static and dynamic emfs and dforce on current carrying conductor, AC operation
More informationHandout 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 informationChapter 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
More informationCalculus Relationships in AP Physics C: Electricity and Magnetism
C: Electricity This chapter focuses on some of the quantitative skills that are important in your C: Mechanics course. These are not all of the skills that you will learn, practice, and apply during the
More informationPhysics 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 information1. An isolated stationary point charge produces around it. a) An electric field only. b) A magnetic field only. c) Electric as well magnetic fields.
1. An isolated stationary point charge produces around it. a) An electric field only. b) A magnetic field only. c) Electric as well magnetic fields. 2. An isolated moving point charge produces around it.
More informationWhat happens when things change. Transient current and voltage relationships in a simple resistive circuit.
Module 4 AC Theory What happens when things change. What you'll learn in Module 4. 4.1 Resistors in DC Circuits Transient events in DC circuits. The difference between Ideal and Practical circuits Transient
More informationChapter 7. Chapter 7. Electric Circuits Fundamentals - Floyd. Copyright 2007 Prentice-Hall
Chapter 7 Magnetic Quantities Magnetic fields are described by drawing flux lines that represent the magnetic field. Where lines are close together, the flux density is higher. Where lines are further
More informationLecture 20. March 22/24 th, Capacitance (Part I) Chapter , Pages
Lecture 0 March /4 th, 005 Capacitance (Part I) Reading: Boylestad s Circuit Analysis, 3 rd Canadian Edition Chapter 10.1-6, Pages 8-94 Assignment: Assignment #10 Due: March 31 st, 005 Preamble: Capacitance
More informationChapter 15 Magnetic Circuits and Transformers
Chapter 15 Magnetic Circuits and Transformers Chapter 15 Magnetic Circuits and Transformers 1. Understand magnetic fields and their interactio with moving charges. 2. Use the right-hand rule to determine
More informationChapter 2: Fundamentals of Magnetism. 8/28/2003 Electromechanical Dynamics 1
Chapter 2: Fundamentals of Magnetism 8/28/2003 Electromechanical Dynamics 1 Magnetic Field Intensity Whenever a magnetic flux, φ, exist in a conductor or component, it is due to the presence of a magnetic
More informationMAGNETIC CIRCUITS. Magnetic Circuits
Basic Electrical Theory What is a magnetic circuit? To better understand magnetic circuits, a basic understanding of the physical qualities of magnetic circuits will be necessary. EO 1.8 EO 1.9 EO 1.10
More informationSliding 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 informationChapter 2 Basics of Electricity and Magnetism
Chapter 2 Basics of Electricity and Magnetism My direct path to the special theory of relativity was mainly determined by the conviction that the electromotive force induced in a conductor moving in a
More informationChapter 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 informationPHYS 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 informationMagnets. 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
More informationENGR 2405 Chapter 6. Capacitors And Inductors
ENGR 2405 Chapter 6 Capacitors And Inductors Overview This chapter will introduce two new linear circuit elements: The capacitor The inductor Unlike resistors, these elements do not dissipate energy They
More informationMagnetic Quantities. Magnetic fields are described by drawing flux lines that represent the magnetic field.
Chapter 7 Magnetic fields are described by drawing flux lines that represent the magnetic field. Where lines are close together, the flux density is higher. Where lines are further apart, the flux density
More informationCHAPTER 29: ELECTROMAGNETIC INDUCTION
CHAPTER 29: ELECTROMAGNETIC INDUCTION So far we have seen that electric charges are the source for both electric and magnetic fields. We have also seen that these fields can exert forces on other electric
More informationSwitched Mode Power Conversion Prof. L. Umanand Department of Electronics System Engineering Indian Institute of Science, Bangalore
Switched Mode Power Conversion Prof. L. Umanand Department of Electronics System Engineering Indian Institute of Science, Bangalore Lecture - 39 Magnetic Design Good day to all of you. Today, we shall
More informationElectromagnetic Induction
Chapter 29 Electromagnetic Induction PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Learning Goals for Chapter 29 Looking forward
More informationPart 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 informationChapter 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 informationElectromagnetic Induction
362 Mechanical Engineering Technician UNIT 7 Electromagnetic Induction Structure 7.1 Introduction 7.2 Faraday s laws of Electromagnetic Induction 7.3. Lenz s law 7.4. Fleming s right and rule 7.5. Self
More informationIntroduction to Electric Circuit Analysis
EE110300 Practice of Electrical and Computer Engineering Lecture 2 and Lecture 4.1 Introduction to Electric Circuit Analysis Prof. Klaus Yung-Jane Hsu 2003/2/20 What Is An Electric Circuit? Electrical
More informationLast 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 informationPhysics 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
More informationCh. 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 informationIE1206 Embedded Electronics Le2
Le1 Le3 Le4 Le6 Le8 IE1206 Embedded Electronics Le2 Ex1 Ex2 Ex4 Ex5 PIC-block Documentation, Seriecom Pulse sensors I, U, R, P, serial and parallel KC1 LAB1 Pulse sensors, Menu program Kirchhoffs laws
More informationPHYS 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
More informationLecture 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 informationRevision Compare Between. Application
evision Compare etween Points of Comparison Series Connection Parallel Connection Drawing otal resistance ( ) = + + 3 3 Potential Difference () = + + 3 = = = 3 Electric Current (I) I = I = I = I 3 I =
More informationAP Physics C. Magnetism - Term 4
AP Physics C Magnetism - Term 4 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the world
More informationFaraday s Law of Induction I
Faraday s Law of Induction I Physics 2415 Lecture 19 Michael Fowler, UVa Today s Topics Magnetic Permeability Faraday s Law of Induction Lenz s Law Paramagnets and Diamagnets Electromagnets Electromagnets
More informationRevision Guide for Chapter 15
Revision Guide for Chapter 15 Contents tudent s Checklist Revision otes Transformer... 4 Electromagnetic induction... 4 Generator... 5 Electric motor... 6 Magnetic field... 8 Magnetic flux... 9 Force on
More informationChapter 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 informationRevision Guide for Chapter 15
Revision Guide for Chapter 15 Contents Revision Checklist Revision otes Transformer...4 Electromagnetic induction...4 Lenz's law...5 Generator...6 Electric motor...7 Magnetic field...9 Magnetic flux...
More informationElectrical Eng. fundamental Lecture 1
Electrical Eng. fundamental Lecture 1 Contact details: h-elhelw@staffs.ac.uk Introduction Electrical systems pervade our lives; they are found in home, school, workplaces, factories,
More informationModule 3: Electromagnetism
Module 3: Electromagnetism Lecture - 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 electromagnetic
More informationIE1206 Embedded Electronics
IE1206 Embedded Electronics Le1 Le3 Le4 Le2 Ex1 Ex2 PIC-block Documentation, Seriecom Pulse sensors I, U, R, P, series and parallel KC1 LAB1 Pulse sensors, Menu program Start of programing task Kirchhoffs
More informationVersion 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 informationInduction 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 informationCapacitors. Charging a Capacitor. Charge and Capacitance. L05: Capacitors and Inductors
L05: Capacitors and Inductors 50 Capacitors 51 Outline of the lecture: Capacitors and capacitance. Energy storage. Capacitance formula. Types of capacitors. Inductors and inductance. Inductance formula.
More informationOutside the solenoid, the field lines are spread apart, and at any given distance from the axis, the field is weak.
Applications of Ampere s Law continued. 2. Field of a solenoid. A solenoid can have many (thousands) of turns, and perhaps many layers of windings. The figure shows a simple solenoid with just a few windings
More informationAQA Physics A-level Section 7: Fields and Their Consequences
AQA Physics A-level Section 7: Fields and Their Consequences Key Points Gravitational fields A force field is a region in which a body experiences a non-contact force. Gravity is a universal force acting
More informationChapter 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 informationReview of Basic Electrical and Magnetic Circuit Concepts EE
Review of Basic Electrical and Magnetic Circuit Concepts EE 442-642 Sinusoidal Linear Circuits: Instantaneous voltage, current and power, rms values Average (real) power, reactive power, apparent power,
More informationChapter 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 informationELECTROMAGNETIC 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
More informationChapter 13 Principles of Electromechanics
Chapter 13 Principles of Electromechanics Jaesung Jang Electrostatics B-H Magnetization Curves & Magnetic Hysteresis 1 Electrostatics & Magnetic Flux The force on a stationary charge q in an electric field
More informationDO 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 informationMagnetic Force on a Moving Charge
Magnetic Force on a Moving Charge Electric charges moving in a magnetic field experience a force due to the magnetic field. Given a charge Q moving with velocity u in a magnetic flux density B, the vector
More informationPHYSICS. 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 informationInduction 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 informationELECTROMAGNETIC INDUCTION
ELECTROMAGNETIC INDUCTION 1. Magnetic Flux 2. Faraday s Experiments 3. Faraday s Laws of Electromagnetic Induction 4. Lenz s Law and Law of Conservation of Energy 5. Expression for Induced emf based on
More informationr 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 information5. ELECTRIC CURRENTS
5. ELECTRIC CURRENTS TOPIC OUTLINE Section Recommended Time Giancoli Section 5.1 Potential Difference, Current, Resistance 5.2 Electric Circuits 3h 19.1, 19.2 6.2 Electric Field and Force 6.3 Magnetic
More informationPhysics 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
More informationPhysics / Higher Physics 1A. Electricity and Magnetism Revision
Physics / Higher Physics 1A Electricity and Magnetism Revision Electric Charges Two kinds of electric charges Called positive and negative Like charges repel Unlike charges attract Coulomb s Law In vector
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Part III. Magnetics 13 Basic Magnetics Theory 14 Inductor Design 15 Transformer Design 1 Chapter
More informationGet Discount Coupons for your Coaching institute and FREE Study Material at ELECTROMAGNETIC INDUCTION
ELECTROMAGNETIC INDUCTION 1. Magnetic Flux 2. Faraday s Experiments 3. Faraday s Laws of Electromagnetic Induction 4. Lenz s Law and Law of Conservation of Energy 5. Expression for Induced emf based on
More informationELECTROMAGNETIC 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 information18 - ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS ( Answers at the end of all questions ) Page 1
( Answers at the end of all questions ) Page ) The self inductance of the motor of an electric fan is 0 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of 8 µ F (
More informationLecture 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 informationFB-DC6 Electric Circuits: Magnetism and Electromagnetism
CREST Foundation Electrical Engineering: DC Electric Circuits Kuphaldt FB-DC6 Electric Circuits: Magnetism and Electromagnetism Contents 1. Electromagnetism 2. Magnetic units of measurement 3. Permeability
More informationSlide 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 informationBasic Electronics. Introductory Lecture Course for. Technology and Instrumentation in Particle Physics Chicago, Illinois June 9-14, 2011
Basic Electronics Introductory Lecture Course for Technology and Instrumentation in Particle Physics 2011 Chicago, Illinois June 9-14, 2011 Presented By Gary Drake Argonne National Laboratory drake@anl.gov
More informationIntroduction to AC Circuits (Capacitors and Inductors)
Introduction to AC Circuits (Capacitors and Inductors) Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/
More informationElectromagnetic 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 informationPhysics 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 informationInductance, 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
More informationRADIO AMATEUR EXAM GENERAL CLASS
RAE-Lessons by 4S7VJ 1 CHAPTER- 2 RADIO AMATEUR EXAM GENERAL CLASS By 4S7VJ 2.1 Sine-wave If a magnet rotates near a coil, an alternating e.m.f. (a.c.) generates in the coil. This e.m.f. gradually increase
More information1 RF components. Cambridge University Press Radio Frequency Integrated Circuits and Systems Hooman Darabi Excerpt More information
9780521190794 Radio Frequency ntegrated Circuits and ystems 1 RF components n this chapter basic components used in RF design are discussed. A detailed modeling and analysis of MO transistors at high frequency
More informationElectromagnetic 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 informationSwitched Mode Power Conversion
Inductors Devices for Efficient Power Conversion Switches Inductors Transformers Capacitors Inductors Inductors Store Energy Inductors Store Energy in a Magnetic Field In Power Converters Energy Storage
More informationPhysics 112. Study Notes for Exam II
Chapter 20 Electric Forces and Fields Physics 112 Study Notes for Exam II 4. Electric Field Fields of + and point charges 5. Both fields and forces obey (vector) superposition Example 20.5; Figure 20.29
More informationPhysics 182. Assignment 4
Physics 182 Assignment 4 1. A dipole (electric or magnetic) in a non-uniform field will in general experience a net force. The electric case was the subject of a problem on the midterm exam; here we examine
More informationElectromagnetism 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 informationPhysics 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 information9-3 Inductance. * We likewise can have self inductance, were a timevarying current in a circuit induces an emf voltage within that same circuit!
/3/004 section 9_3 Inductance / 9-3 Inductance Reading Assignment: pp. 90-86 * A transformer is an example of mutual inductance, where a time-varying current in one circuit (i.e., the primary) induces
More informationLecture 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 informationPhysics 11b Lecture #13
Physics 11b Lecture #13 Faraday s Law S&J Chapter 31 Midterm #2 Midterm #2 will be on April 7th by popular vote Covers lectures #8 through #14 inclusive Textbook chapters from 27 up to 32.4 There will
More informationGood Luck! Exam 2 Review Phys 222 Supplemental Instruction SUNDAY SESSION AS NORMAL, INFORMAL Q/A
Good Luck! Exam 2 Review Phys 222 Supplemental Instruction SUNDAY SESSION AS NORMAL, INFORMAL Q/A The correct solution process is the right answer Do you know all the following? Circuits Current, Voltage,
More informationChapter 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 informationCOLLEGE PHYSICS Chapter 23 ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES
COLLEGE PHYSICS Chapter 23 ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES Induced emf: Faraday s Law and Lenz s Law We observe that, when a magnet is moved near a conducting loop,
More informationElectricity & 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 informationTutorial Sheet IV. Fig. IV_2.
Tutorial Sheet IV 1. Two identical inductors 1 H each are connected in series as shown. Deduce the combined inductance. If a third and then a fourth are similarly connected in series with this combined
More informationAP Physics C. Electricity - Term 3
AP Physics C Electricity - Term 3 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the
More information