The March/April Morseman Problem

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "The March/April Morseman Problem"

Transcription

1 The Problem as stated was: The March/April Morseman Problem A toroidal transformer is used in directional coupler versions of an SWR bridge. The primary winding is the single wire running through the toroid, the secondary is wound with equal-spaced turns around the toroid. A diagram of the complete coupler, and an explanation of how it works, can be downloaded from my website 1 The figure shown in the column is figure 3, on the following page. The first diagram showing the coupler circuit from my website document is figure 1. Figure 1: The Bruene SWR detector, showing centre-tapped toroidal transformer. The mutual inductance between primary and secondary is found using Faraday s Law, with a straightforward integration. Questions: How can the primary wire shown be a winding? (A winding must be a closed loop, but this is just a single wire.) The wire is always shown threading through the exact centre of the toroid. Will it still work if it goes through off-centre? How will the mutual inductance change if this wire is off-centre? Before tackling these questions, we revise how mutual inductance is defined and calculated. Mutual Inductance Mutual inductance is a joint property of two closed conducting loops. Figure 2 shows two coils in proximity. Coil 1 carries a current, giving rise to the magnetic field shown by the field lines. Some of this field passes through coil 2. If the current in the first coil changes, the flux intercepted by the second coil will also change, and by Faraday s Law, a voltage will also be induced in its windings. This flux coupling is utilised in all transformers. The degree of coupling is a function of the geometry of the system, and is specified by their Mutual Inductance. Let the total flux passing through the windings of coil 1, having inductance L 1, be Φ 1. Let the total flux passing through coil 2 be Φ 2, and the voltage induced in its winding be V 2. Using Faraday s Law, Inductance is defined as L = dφ 1 = dφ 1. (1) 1 Download from the link on my website to The Bruene Directional Coupler and Transmission Lines. 1

2 Figure 2: Two coils in proximity coupled by mutual inductance. rearranging, dφ 1 = L 1 and V 2 = dφ 2 The negative signs imply that the induced voltage in each case opposes the flux increase. Let the proportion of flux intercepted by coil 2 be α. Then (2) (3) Φ 2 = αφ 1 (4) dφ 2 = α dφ 1 = +αl 1 = M (6) where M = αl 1 = the mutual inductance (7) (5) then M = dφ 2 (8) or, for a linear medium, M = Φ 2 I 1 (9) and the voltage induced across L 2 is V 2 = M Mutual Inductance of a Toroidal Coil Threaded by a Wire. In general mutual inductance is difficult to calculate. Only a few configurations, including that of the central wire toroidal transformer described here, are analytically tractable. Figure 3 shows such a toroid around which a coil (windings not shown) is wound. The toroid is threaded by a wire passing normally through its exact centre, part of a closed loop through which current flows. When an rf current flows in the wire, mutual inductance between the wire and the toroidal winding cause an induced voltage to form across the toroidal winding. The toroid has a rectangular cross-sectional dimensions h and W, and inner radius R. For computational simplicity, the wire is assumed to be infinitely long, so that its magnetic field inside the toroid can be calculated using Ampere s Law. This law states that B.dl = µi (11) l In words, this says that the magnetic field component B.dl, integrated over any complete closed path l around a current I flowing anywhere through this path, is proportional to the current, with constant of proportionality µ, the permeability of the medium. (10) 2

3 Figure 3: An infinitely long straight wire passing through the centre of a toroid. Assume that a current I flows in the straight wire. The magnetic field lines due to the wire will be symmetric and circular, centred on the wire. Those between radii of R and R + W will pass through the toroid. We can calculate the flux through the toroid using this integration, evaluating the magnetic field using Ampere s Law. At radius r, the path length is r, and B is constant along it, so from Ampere s Law, rb(r) = µi (12) Re-arranging, the magnetic field magnitude at radius r is B(r) = µi (13) r The flux passing through a small cross-section of the toroid from radius r to r + dr will be dφ 2 = µinh r integrating, Φ 2 = µinh Φ 2 = µinh but from equation 10, M = Φ 2 I so M = µnh dr (14) R+W dr (15) R r ( log e 1 + W ) (16) R log e ( 1 + W ) R Both plots of field-lines shown next were produced using a numerical field-calculation program (see the Appendix) because analytic calculation for the right-hand case is analytically intractible. Figure 4, left, shows the magnetic field lines surrounding a centrally placed wire through the toroid having a relative permeability of 20 (that is, µ = 20µ o. This value is rather low for a toroid used as a balun or SWR bridge detector, but this low value shows the lines better). The current in the wire is flowing into the page. In this case, all field lines are circular, and are either completely inside or outside the toroid. Those inside are closer together than those outside, indicating that the field strength is higher inside the toroid. The strength of the field is the same at all points in the toroid. Figure 4, right, shows the field-lines resulting from an off-centre central wire. The field-lines from the wire are circular at low radii, but as the radius increases some of them cut the surface of the toroid, where the permeability abruptly increases by a factor of 20. On entering the toroid, they are bent away from the normal, on leaving, towards the normal. Each field-line is still continuous. The boundary conditions between the media, used to find the angle of diffraction, are derived from the two Maxwell equations (17) (18). B = 0 (19) B = J (20) 3

4 In words, the first one states that the divergence of the magnetic field is zero, the second states that the curl of the magnetic field equals the current density at the point where the curl is calculated. The macroscopic form of this law is Ampere s Law, equation 11 above. Figure 4: Magnetic field-lines induced in the toroid by Left: A central wire, Right: An off-centre wire. The diffraction boundary conditions for field-lines travelling between magnetic media are described in many references, for example The right-hand plot of figure 4 also shows that the field-lines inside the toroid are spaced more closely in the section nearest the wire, than those in the section directly opposite. This indicates that the field inside the toroid closest to the wire is higher than that directly opposite. In this figure, the difference in magnitude is about a factor of 2. Furthermore, the changing spacing of the field lines shows that magnetic intensity varies continuously around, and inside the toroid. The Effect of Wire Position on the Toroid s Inductance. If an evenly-spaced coil is wound around the toroid, its inductance turns out to be exactly the same for both situations. Physically, you can see this is reasonable because the larger inductance induced by the closely-spaced lines in the toroid near the wire might be exactly balanced by the smaller inductance induced by the more widely-spaced lines further away. And in fact, it is. Mathematically, this is a consequence of Ampere s law, stated again as B.dl = µi (21) l This, paraphrased, states that the total magnetic intensity integrated around any closed path is always proportional to the current flowing through the path. It does not matter where inside the loop the current passes! If the coil is wound uniformly around the whole toroid, this integrated intensity is therefore the same for both cases shown in figure 4, and since this total intensity is what determines the inductance, the inductance will also be the same! 4

5 Note, however, that the integration is not along a field line inside the toroid, since some lines enter and exit the toroid, and do not follow radial paths inside it. The integration is along a circular (radial) path, using the component of the field line resolved along this path. It s the constantly-changing direction of this component which makes an analytic solution for this case so intractable. But there s an interesting wrinkle to this, which affects the operation of the Bruene SWR bridge, shown in figure 1. The Bruene SWR Bridge A modified version of this toroidal transformer is the basis of the SWR measuring technique used in this Bridge, shown in figure 1. Here, the winding is also wound completely around the toroid, but is centre-tapped, and one half is used to induce a voltage proportional to the forward current, the other half the reverse current Assume that the centre-tap is positioned half-way between the maximum and minimum field intensity positions, that is, at an angle of 90 o to the line joining the wire in figure 4, right, to the closest point of the toroid (at about the 2 oclock position.) The lower coil-half (nearest the wire) will then have a higher mutual inductance with the wire than the upper coil-half (furthest from the wire), because the integrated field intensity through the lower portion will be higher than that through the upper. Hence, even if the detection components (diode rectifier and smoothing) are identical in the forward and backward circuits, the voltages induced in the two halves will always be unequal. In practice, this effect is small, and does not matter anyway, because adjustable resistances shown as R cal in figure 1 are always included to compensate for this effect - and for any difference in the diodes, capacitors and voltmeters used in the two sections. Note that figure 1 also shows that one of the capacitors used in the voltage divider section, at left, is variable. This is adjusted at the factory to make the reverse voltage zero when a pure resistance equal to the characteristic impedance of the line to be measured is used to terminate the bridge. You can also adjust this capacitor if you suspect the calibration, though most instructional pamphlets don t mention this - mine, for my MFJ bridges, don t, anyway. Appendix The plots of figure 1 were made using the program Vizimag, downloadable from You have to pay $39.75 (US) for a single-user license, but you can use it free for 30 days. The program has an easily-mastered graphical interface, and enables you to calculate, plot, and read magnetic field magnitudes and directions at any point for a variety of configurations involving wires, toroids, magnets, magnetic materials. You can also make animations! Gary ZL1AN 5

* Self-inductance * Mutual inductance * Transformers. PPT No. 32

* Self-inductance * Mutual inductance * Transformers. PPT No. 32 * Self-inductance * Mutual inductance * Transformers PPT No. 32 Inductance According to Faraday s Electromagnetic Induction law, induction of an electromotive force occurs in a circuit by varying the magnetic

More information

Eðlisfræði 2, vor 2007

Eðlisfræði 2, vor 2007 [ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 29a. Electromagnetic Induction Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the

More information

Electromagnetic Induction

Electromagnetic Induction Electromagnetic Induction Lecture 29: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Mutual Inductance In the last lecture, we enunciated the Faraday s law according to

More information

Chapter 30 Inductance

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

More information

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

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H). INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes

More information

Electric Engineering II EE 326 Lecture 4 & 5

Electric Engineering II EE 326 Lecture 4 & 5 Electric Engineering II EE 326 Lecture 4 & 5 Transformers ١ Transformers Electrical transformers have many applications: Step up voltages (for electrical energy transmission with

More information

Name: Lab Partner: Section: The purpose of this lab is to study induction. Faraday s law of induction and Lenz s law will be explored.

Name: Lab Partner: Section: The purpose of this lab is to study induction. Faraday s law of induction and Lenz s law will be explored. Chapter 8 Induction - Faraday s Law Name: Lab Partner: Section: 8.1 Purpose The purpose of this lab is to study induction. Faraday s law of induction and Lenz s law will be explored. 8.2 Introduction It

More information

Faraday s Law & Maxwell s Equations (Griffiths Chapter 7: Sections 2-3) B t da = S

Faraday s Law & Maxwell s Equations (Griffiths Chapter 7: Sections 2-3) B t da = S Dr. Alain Brizard Electromagnetic Theory I PY 3 Faraday s Law & Maxwell s Equations Griffiths Chapter 7: Sections -3 Electromagnetic Induction The flux rule states that a changing magnetic flux Φ B = S

More information

Chapter 9: Ideal Transformer. 10/9/2003 Electromechanical Dynamics 1

Chapter 9: Ideal Transformer. 10/9/2003 Electromechanical Dynamics 1 Chapter 9: Ideal Transformer 10/9/003 Electromechanical Dynamics 1 Introduction Transformers are one of the most useful electrical devices provides a change in voltage and current levels provides galvanic

More information

Mutual inductance. Resources and methods for learning about these subjects (list a few here, in preparation for your research):

Mutual inductance. Resources and methods for learning about these subjects (list a few here, in preparation for your research): Mutual inductance This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,

More information

* Biot Savart s Law- Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B. PPT No.

* Biot Savart s Law- Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B. PPT No. * Biot Savart s Law- Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B PPT No. 17 Biot Savart s Law A straight infinitely long wire is carrying

More information

Chap 21. Electromagnetic Induction

Chap 21. Electromagnetic Induction Chap 21. Electromagnetic Induction Sec. 1 - Magnetic field Magnetic fields are produced by electric currents: They can be macroscopic currents in wires. They can be microscopic currents ex: with electrons

More information

RUPHYS ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman

RUPHYS ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman Signed in as Jolie Cizewski, Instructor Help Sign Out RUPHYS2272014 ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman Course Home Assignments Roster

More information

Supplementary Notes on Transformers

Supplementary Notes on Transformers Supplementary Notes on Transformers A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors the transformer's coils. Figure 1 illustrates

More information

Electrical Machines II. Week 1: Construction and theory of operation of single phase transformer

Electrical Machines II. Week 1: Construction and theory of operation of single phase transformer Electrical Machines II Week 1: Construction and theory of operation of single phase transformer Transformers Overview A transformer changes ac electric power at one frequency and voltage level to ac electric

More information

AP Physics C Chapter 23 Notes Yockers Faraday s Law, Inductance, and Maxwell s Equations

AP Physics C Chapter 23 Notes Yockers Faraday s Law, Inductance, and Maxwell s Equations AP Physics C Chapter 3 Notes Yockers Faraday s aw, Inductance, and Maxwell s Equations Faraday s aw of Induction - induced current a metal wire moved in a uniform magnetic field - the charges (electrons)

More information

Fall 12 PHY 122 Homework Solutions #10

Fall 12 PHY 122 Homework Solutions #10 Fall 12 PHY 122 Homework Solutions #10 HW10: Ch.30 Q5, 8, 15,17, 19 P 1, 3, 9, 18, 34, 36, 42, 51, 66 Chapter 30 Question 5 If you are given a fixed length of wire, how would you shape it to obtain the

More information

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

Chapter 20. Magnetic Induction Changing Magnetic Fields yield Changing Electric Fields Chapter 20 Magnetic Induction Changing Magnetic Fields yield Changing Electric Fields Introduction The motion of a magnet can induce current in practical ways. If a credit card has a magnet strip on its

More information

A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle

A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle Page 1 of 15 Abstract: The wireless power transfer link between two coils is determined by the properties of the

More information

Objectives for the standardized exam

Objectives for the standardized exam III. ELECTRICITY AND MAGNETISM A. Electrostatics 1. Charge and Coulomb s Law a) Students should understand the concept of electric charge, so they can: (1) Describe the types of charge and the attraction

More information

physics 112N electromagnetic induction

physics 112N electromagnetic induction physics 112N electromagnetic induction experimental basis of induction! seems we can induce a current in a loop with a changing magnetic field physics 112N 2 magnetic flux! useful to define a quantity

More information

DOING PHYSICS WITH MATLAB ELECTROMAGNETIC INDUCTION FARADAY S LAW MUTUAL & SELF INDUCTANCE

DOING PHYSICS WITH MATLAB ELECTROMAGNETIC INDUCTION FARADAY S LAW MUTUAL & SELF INDUCTANCE DOING PHYSICS WITH MATLAB ELECTROMAGNETIC INDUCTION FARADAY S LAW MUTUAL & SELF INDUCTANCE Ian Cooper School of Physics, University of Sydney ian.cooper@sydney.edu.au DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS

More information

2. TRANSFORMERS. The main learning objectives for this chapter are listed below. Use equivalent circuits to determine voltages and currents.

2. TRANSFORMERS. The main learning objectives for this chapter are listed below. Use equivalent circuits to determine voltages and currents. . TRANSFORMERS Transformers are commonly used in applications which require the conversion of AC voltage from one voltage level to another. There are two broad categories of transformers: electronic transformers,

More information

Faraday's Law and Inductance

Faraday's Law and Inductance Page 1 of 8 test2labh_status.txt Use Internet Explorer for this laboratory. Save your work often. NADN ID: guest49 Section Number: guest All Team Members: Your Name: SP212 Lab: Faraday's Law and Inductance

More information

INTRODUCTION SELF INDUCTANCE. Introduction. Self inductance. Mutual inductance. Transformer. RLC circuits. AC circuits

INTRODUCTION SELF INDUCTANCE. Introduction. Self inductance. Mutual inductance. Transformer. RLC circuits. AC circuits Chapter 13 INDUCTANCE Introduction Self inductance Mutual inductance Transformer RLC circuits AC circuits Magnetic energy Summary INTRODUCTION Faraday s important contribution was his discovery that achangingmagneticflux

More information

Chapter 29 Electromagnetic Induction

Chapter 29 Electromagnetic Induction Chapter 29 Electromagnetic Induction - Induction Experiments - Faraday s Law - Lenz s Law - Motional Electromotive Force - Induced Electric Fields - Eddy Currents - Displacement Current and Maxwell s Equations

More information

Chapter 27 Magnetic Induction. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

Chapter 27 Magnetic Induction. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Chapter 27 Magnetic Induction Motional EMF Consider a conductor in a B-field moving to the right. In which direction will an electron in the bar experience a magnetic force? V e - V The electrons in the

More information

Last time : energy storage elements capacitor.

Last time : energy storage elements capacitor. Last time : energy storage elements capacitor. Charge on plates Energy stored in the form of electric field Passive sign convention Vlt Voltage drop across real capacitor can not change abruptly because

More information

Chapter 14 Magnets and

Chapter 14 Magnets and Chapter 14 Magnets and Electromagnetism How do magnets work? What is the Earth s magnetic field? Is the magnetic force similar to the electrostatic force? Magnets and the Magnetic Force! We are generally

More information

Questions. Question 1

Questions. Question 1 Question 1 Questions Explain why transformers are used extensively in long-distance power distribution systems. What advantage do they lend to a power system? file 02213 Question 2 Are the transformers

More information

PHYS 155: Final Tutorial

PHYS 155: Final Tutorial Final Tutorial Saskatoon Engineering Students Society eric.peach@usask.ca April 13, 2015 Overview 1 2 3 4 5 6 7 Tutorial Slides These slides have been posted: sess.usask.ca homepage.usask.ca/esp991/ Section

More information

Electromagnetic Induction. Physics 231 Lecture 9-1

Electromagnetic Induction. Physics 231 Lecture 9-1 Electromagnetic Induction Physics 231 Lecture 9-1 Induced Current Past experiments with magnetism have shown the following When a magnet is moved towards or away from a circuit, there is an induced current

More information

Applying Faraday s law to both the primary and the secondary (noting the possibility of sources applied to either winding), yields

Applying Faraday s law to both the primary and the secondary (noting the possibility of sources applied to either winding), yields TRANSFORMERS Transformers are key elements in power systems. In order to effectively transmit power over long distances without prohibitive line losses, the voltage from the generator (a maximum of output

More information

Eðlisfræði 2, vor 2007

Eðlisfræði 2, vor 2007 [ Assignment View ] [ Print ] Eðlisfræði 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has

More information

Faraday s Law and Inductance

Faraday s Law and Inductance Historical Overview Faraday s Law and Inductance So far studied electric fields due to stationary charges and magentic fields due to moving charges. Now study electric field due to a changing magnetic

More information

Physics Notes for Class 12 Chapter 4 Moving Charges and Magnetrism

Physics Notes for Class 12 Chapter 4 Moving Charges and Magnetrism 1 P a g e Physics Notes for Class 12 Chapter 4 Moving Charges and Magnetrism Oersted s Experiment A magnetic field is produced in the surrounding of any current carrying conductor. The direction of this

More information

Physics 6C, Summer 2006 Homework 1 Solutions F 4

Physics 6C, Summer 2006 Homework 1 Solutions F 4 Physics 6C, Summer 006 Homework 1 Solutions All problems are from the nd edition of Walker. Numerical values are different for each student. Chapter Conceptual Questions 18. Consider the four wires shown

More information

5K10.20 Induction Coil with Magnet, Galvanometer

5K10.20 Induction Coil with Magnet, Galvanometer 5K10.20 Induction Coil with Magnet, Galvanometer Abstract When a magnet is moved through a coil of wire, a current is induced in the coil. A galvanometer connected to the coil measures this induced current.

More information

Wireless Power Transfer RAQUEL MONTALVO CANO. Departamento de electricidad. Univ. Carlos III de Madrid

Wireless Power Transfer RAQUEL MONTALVO CANO. Departamento de electricidad. Univ. Carlos III de Madrid Wireless Power Transfer RAQUEL MONTALVO CANO Departamento de electricidad. Univ. Carlos III de Madrid Leganés, Spain 2012 Department of Energy and Environment Division of Electric Power Engineering CHALMERS

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 23.1 Induced EMF 23.2 Magnetic Flux 23.3 Faraday s Law of Induction 23.4 Lenz s Law 23.5 Mechanical Work and Electrical Energy 23.6 Generators and

More information

Induced voltage CPD. Practical Activity on Induced Voltage

Induced voltage CPD. Practical Activity on Induced Voltage Practical Activity on Induced Voltage Introduction In this experiment you will investigate the variation of induced emf in a coil as a magnet is dropped through the coil. The passage of the magnet through

More information

" - angle between l and a R

 - angle between l and a R Magnetostatic Fields According to Coulomb s law, any distribution of stationary charge produces a static electric field (electrostatic field). The analogous equation to Coulomb s law for electric fields

More information

Coupled Inductors. Introducing Coupled Inductors

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

More information

STUDY OF IDEAL TRANSFORMER AND PRACTICAL TRANSFORMER

STUDY OF IDEAL TRANSFORMER AND PRACTICAL TRANSFORMER STUDY OF IDEAL TRANSFORMER AND PRACTICAL TRANSFORMER RUBY DHANKAR, SAPNA KAMRA,VISHAL JANGRA Abstract- This paper proposes the study of real and ideal transformer. It also explains load, no-load conditions

More information

Inductive and Magnetic Sensors

Inductive and Magnetic Sensors Chapter 12 Inductive and Magnetic Sensors 12.1 Inductive Sensors A number of the actuators developed in previous chapters depend on the variation of reluctance with changes in angle or displacement. Since

More information

Module 3 : MAGNETIC FIELD Lecture 15 : Biot- Savarts' Law

Module 3 : MAGNETIC FIELD Lecture 15 : Biot- Savarts' Law Module 3 : MAGNETIC FIELD Lecture 15 : Biot- Savarts' Law Objectives In this lecture you will learn the following Study Biot-Savart's law Calculate magnetic field of induction due to some simple current

More information

Electromagnetic Induction

Electromagnetic Induction . Electromagnetic Induction Concepts and Principles Creating Electrical Energy When electric charges move, their electric fields vary. In the previous two chapters we considered moving electric charges

More information

Solution Derivations for Capa #10

Solution Derivations for Capa #10 Solution Derivations for Capa #10 1) A 1000-turn loop (radius = 0.038 m) of wire is connected to a (25 Ω) resistor as shown in the figure. A magnetic field is directed perpendicular to the plane of the

More information

ELET 4143 Electrical Machines and Controls

ELET 4143 Electrical Machines and Controls ELET 4143 Electrical Machines and Controls Electromagnetism Spring 2008 Energy in an Inductor A coils stores in its magnetic field when it carries a current I The energy is given by: W = ½ L I 2 W = Energy

More information

Outline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... )

Outline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... ) Outline Systems and Signals 214 / 244 & Energy Systems 244 / 344 Inductance, Leakage Inductance, Mutual Inductance & Transformers 1 Inductor revision Ideal Inductor Non-Ideal Inductor Dr. P.J. Randewijk

More information

LAB 8: Electron Charge-to-Mass Ratio

LAB 8: Electron Charge-to-Mass Ratio Name Date Partner(s) OBJECTIVES LAB 8: Electron Charge-to-Mass Ratio To understand how electric and magnetic fields impact an electron beam To experimentally determine the electron charge-to-mass ratio.

More information

This Set o Slides - Day 20, Friday, Feb 19

This Set o Slides - Day 20, Friday, Feb 19 This Set o Slides - Day 20, Friday, Feb 19 Magnetic Field of Moving Charge or Current Biot-Savart Law Cross Product. Biot-Savart Law as cross product. More right hand rules. Three total! Similar but different!

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

Eðlisfræði 2, vor 2007

Eðlisfræði 2, vor 2007 [ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 28. Sources of Magnetic Field Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the deadline

More information

Open circuit and short circuit tests on single phase transformer

Open circuit and short circuit tests on single phase transformer 1 Aim Experiment No: 2 Open circuit and short circuit tests on single phase transformer To understand the basic working principle of a transformer. To obtain the equivalent circuit parameters from OC and

More information

Chapter 16. Current Transformer Design. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Chapter 16. Current Transformer Design. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. Chapter 16 Current Transformer Design Table of Contents 1. Introduction 2. Analysis of the Input Current Component 3. Unique to a Current Transformer 4. Current Transformer Circuit Applications 5. Current

More information

Electrical Circuits (2)

Electrical Circuits (2) Electrical Circuits (2) Lecture 5 Magnetically Coupled Circuits Dr.Eng. Basem ElHalawany Magnetically Coupled Circuits The circuits we have considered so far may be regarded as conductively coupled, because

More information

Electromagnetic Induction

Electromagnetic Induction Electromagnetic Induction "Concepts without factual content are empty; sense data without concepts are blind... The understanding cannot see. The senses cannot think. By their union only can knowledge

More information

6.1 The Capacitor 6.2 The Inductor 6.3 Series-Parallel Combinations of Capacitance and Inductance 6.4 Mutual Inductance

6.1 The Capacitor 6.2 The Inductor 6.3 Series-Parallel Combinations of Capacitance and Inductance 6.4 Mutual Inductance CAPACITACE, IDUCTACE, AD MUTUA IDUCTACE 6. The Capacitor 6. The Inductor 6.3 Series-Parallel Combinations of Capacitance and Inductance 6. The Capacitor In this chapter, two new and important passive linear

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

Quality Transformer and Electronics, Inc. Introduction to Transformers. By Quality Transformer and Electronics Engineering & Sales Staff

Quality Transformer and Electronics, Inc. Introduction to Transformers. By Quality Transformer and Electronics Engineering & Sales Staff 2014 Introduction to Transformers By Quality Transformer and Electronics Engineering & Sales Staff Introduction to Transformers Since the widespread distribution of electricity has existed, so have transformers.

More information

Faraday s Law of Induction

Faraday s Law of Induction Faraday s Law of Induction Potential drop along the closed contour is minus the rate of change of magnetic flu. We can change the magnetic flu in several ways including changing the magnitude of the magnetic

More information

PHY2049 Exam #2 Solutions Fall 2012

PHY2049 Exam #2 Solutions Fall 2012 PHY2049 Exam #2 Solutions Fall 2012 1. The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial segments. The circuits

More information

MOVING CHARGES AND MAGNETISM

MOVING CHARGES AND MAGNETISM MOVING CHARGES AND MAGNETISM 1. A circular Coil of 50 turns and radius 0.2m carries of current of 12A Find (a). magnetic field at the centre of the coil and (b) magnetic moment associated with it. 3 scores

More information

A Study of Linear Variable Differential Transformers in MATLAB

A Study of Linear Variable Differential Transformers in MATLAB A Study of Linear Variable Differential Transformers in MATLAB Alicia Alarie Jacob Tutmaher April 25, 2011 Abstract The purpose of this lab was to test Faraday s Law using a Linear Variable Differential

More information

Special topics in Physics: Electricity and Magnetism

Special topics in Physics: Electricity and Magnetism Parkland College A with Honors Projects Honors Program 2011 Special topics in Physics: Electricity and Magnetism Ken Smith Parkland College Recommended Citation Smith, Ken, "Special topics in Physics:

More information

Experimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION ( )

Experimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION ( ) a. Using Faraday s law: Experimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION The overall sign will not be graded. For the current, we use the extensive hints in the

More information

2. Consider a dipole AB of dipole moment p placed at an angle θ in an uniform electric field E

2. Consider a dipole AB of dipole moment p placed at an angle θ in an uniform electric field E 1) Field due to an infinite long straight charged wire Consider an uniformly charged wire of infinite length having a constant linear charge density λ (charge per unit length). 2. Consider a dipole AB

More information

Ampere's Law. Introduction. times the current enclosed in that loop: Ampere's Law states that the line integral of B and dl over a closed path is 0

Ampere's Law. Introduction. times the current enclosed in that loop: Ampere's Law states that the line integral of B and dl over a closed path is 0 1 Ampere's Law Purpose: To investigate Ampere's Law by measuring how magnetic field varies over a closed path; to examine how magnetic field depends upon current. Apparatus: Solenoid and path integral

More information

ELECTROMAGNETIC INDUCTION (Y&F Chapters 30, 31; Ohanian Chapter 32) The Electric and magnetic fields are inter-related

ELECTROMAGNETIC INDUCTION (Y&F Chapters 30, 31; Ohanian Chapter 32) The Electric and magnetic fields are inter-related EMF Handout 9: Electromagnetic Induction 1 ELECTROMAGNETIC INDUCTION (Y&F Chapters 30, 31; Ohanian Chapter 32) This handout covers: Motional emf and the electric generator Electromagnetic Induction and

More information

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

Question Bank. 1. Electromagnetism 2. Magnetic Effects of an Electric Current 3. Electromagnetic Induction 1. Electromagnetism 2. Magnetic Effects of an Electric Current 3. Electromagnetic Induction 1. Diagram below shows a freely suspended magnetic needle. A copper wire is held parallel to the axis of magnetic

More information

Electromagnetism Laws and Equations

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

More information

Faraday s Law Challenge Problem Solutions

Faraday s Law Challenge Problem Solutions Faraday s Law Challenge Problem Solutions Problem 1: A coil of wire is above a magnet whose north pole is pointing up. For current, counterclockwise when viewed from above is positive. For flux, upwards

More information

Coupling Factor Calculation of Low Frequency RFID Systems by the Mutual Inductance Effective Permeability Method

Coupling Factor Calculation of Low Frequency RFID Systems by the Mutual Inductance Effective Permeability Method Coupling Factor Calculation of Low Frequency RFID Systems by the Mutual Inductance Effective Permeability Method P. Csurgai, M. Kuczmann Szécheny István University, Lab. Of Electromagentic Fields, Dept.

More information

Physics 2220 Module 09 Homework

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

More information

Chapter 31. Faraday s Law

Chapter 31. Faraday s Law Chapter 31 Faraday s Law Michael Faraday 1791 1867 British physicist and chemist Great experimental scientist Contributions to early electricity include: Invention of motor, generator, and transformer

More information

MAGNETIC FIELDS AND FORCES

MAGNETIC FIELDS AND FORCES PHYSICS 120 : ELECTRICITY AND MAGNETISM TUTORIAL QUESTIONS MAGNETIC IELDS AND ORCES Question 96 A charge of 12.0 ñc, travelling with a speed of 9.00 10 6 ms 1 in a direction perpendicular to a magnetic

More information

Sources of Magnetic Field: Summary

Sources of Magnetic Field: Summary Sources of Magnetic Field: Summary Single Moving Charge (Biot-Savart for a charge): Steady Current in a Wire (Biot-Savart for current): Infinite Straight Wire: Direction is from the Right Hand Rule The

More information

IMPEDANCE and NETWORKS. Kirchoff s laws. Charge inside metals. Skin effect. Impedance, Resistance, Capacitance, Inductance

IMPEDANCE and NETWORKS. Kirchoff s laws. Charge inside metals. Skin effect. Impedance, Resistance, Capacitance, Inductance IMPEDANCE and NETWORKS Kirchoff s laws Charge inside metals Skin effect Impedance, Resistance, Capacitance, Inductance Mutual Inductance, Transformers Stray impedance 1 ENGN4545/ENGN6545: Radiofrequency

More information

Inductors & Inductance. Electronic Components

Inductors & Inductance. Electronic Components Electronic Components Induction In 1824, Oersted discovered that current passing though a coil created a magnetic field capable of shifting a compass needle. Seven years later, Faraday and Henry discovered

More information

Solution Derivations for Capa #11

Solution Derivations for Capa #11 Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5.0 V, = 155 Ω, L = 8.400 10 2 H. In the diagram above, what is the voltage across the

More information

Diodes have an arrow showing the direction of the flow.

Diodes have an arrow showing the direction of the flow. The Big Idea Modern circuitry depends on much more than just resistors and capacitors. The circuits in your computer, cell phone, Ipod depend on circuit elements called diodes, inductors, transistors,

More information

Magnetic Field of a Circular Coil Lab 12

Magnetic Field of a Circular Coil Lab 12 HB 11-26-07 Magnetic Field of a Circular Coil Lab 12 1 Magnetic Field of a Circular Coil Lab 12 Equipment- coil apparatus, BK Precision 2120B oscilloscope, Fluke multimeter, Wavetek FG3C function generator,

More information

The terminology used by Würth Elektronik clearly distinguishes between inductors and EMC ferrites in regard to the quality of the inductor:

The terminology used by Würth Elektronik clearly distinguishes between inductors and EMC ferrites in regard to the quality of the inductor: 1.8 Differentiating EMC ferrite inductor The terminology used by Würth Elektronik clearly distinguishes between inductors and EMC ferrites in regard to the quality of the inductor: EMC ferrites are based

More information

Faraday s and Lenz s Law: Induction

Faraday s and Lenz s Law: Induction Lab #18 Induction page 1 Faraday s and Lenz s Law: Induction Reading: Giambatista, Richardson, and Richardson Chapter 20 (20.1-20.9). Summary: In order for power stations to provide electrical current

More information

Chapter 30 - Magnetic Fields and Torque. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 30 - Magnetic Fields and Torque. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapter 30 - Magnetic Fields and Torque A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should

More information

Tuesday, 9 August 2016

Tuesday, 9 August 2016 Tuesday, 9 August 2016 Conceptual Problem 34.10 a When the switch on the left is closed, which direction does current flow in the meter on the right: 1. Right to left 2. Left to right 3. There is no induced

More information

Mutual Inductance and Transformers F3 3. r L = ω o

Mutual Inductance and Transformers F3 3. r L = ω o utual Inductance and Transformers F3 1 utual Inductance & Transformers If a current, i 1, flows in a coil or circuit then it produces a magnetic field. Some of the magnetic flux may link a second coil

More information

Chapter 14: Magnets and Electromagnetism

Chapter 14: Magnets and Electromagnetism Chapter 14: Magnets and Electromagnetism 1. Electrons flow around a circular wire loop in a horizontal plane, in a direction that is clockwise when viewed from above. This causes a magnetic field. Inside

More information

ELECTROMAGNETISM I. CAUSES OF MAGNETISM

ELECTROMAGNETISM I. CAUSES OF MAGNETISM I. CAUSES OF MAGNETISM ELECTROMAGNETISM 1. Moving electric fields (moving charges) cause magnetism. Yes, that current moving in electric circuits cause a magnetic field. More later! 2. Elementary nature

More information

The Smith chart. Smith chart components. The normalized impedance line CHAPTER

The Smith chart. Smith chart components. The normalized impedance line CHAPTER 26 CHAPTER The Smith chart The mathematics of transmission lines, and certain other devices, becomes cumbersome at times, especially when dealing with complex impedances and nonstandard situations. In

More information

Magnetic Forces and Magnetic Fields

Magnetic Forces and Magnetic Fields 1 Magnets Magnets are metallic objects, mostly made out of iron, which attract other iron containing objects (nails) etc. Magnets orient themselves in roughly a north - south direction if they are allowed

More information

Coil Testing in a Manufacturing Environment

Coil Testing in a Manufacturing Environment Coil Testing in a Manufacturing Environment by Anthony Pretto, International Electro-Magnetics, Inc. Quality control is an integral part of any manufacturing process. As a part of that process, it is important

More information

A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS

A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS Joseph J. Stupak Jr, Oersted Technology Tualatin, Oregon (reprinted from IMCSD 24th Annual Proceedings 1995) ABSTRACT The

More information

Linear DC Motors. 15.1 Magnetic Flux. 15.1.1 Permanent Bar Magnets

Linear DC Motors. 15.1 Magnetic Flux. 15.1.1 Permanent Bar Magnets Linear DC Motors The purpose of this supplement is to present the basic material needed to understand the operation of simple DC motors. This is intended to be used as the reference material for the linear

More information

15-Non-Ideal Single Phase Transformers. ECEGR 450 Electromechanical Energy Conversion

15-Non-Ideal Single Phase Transformers. ECEGR 450 Electromechanical Energy Conversion 15NonIdeal Single Phase Transformers ECEGR 450 Electromechanical Energy Conversion Magnetizing Reactance Core Resistance Leakage Reactance Winding Resistance Overview Dr. Louie 2 Questions What are the

More information

Your Comments. I got so confused with Faraday's Law and Lenz's Law... AREN'T THESE TWO LAWS SUPPOSED TO MEAN THE SAME THING???

Your Comments. I got so confused with Faraday's Law and Lenz's Law... AREN'T THESE TWO LAWS SUPPOSED TO MEAN THE SAME THING??? Your Comments There were some parts of this prelecture I grasped well while other parts like the generator and the loops I still have trouble with. Can you please clarify how Faraday's and Lenz's law are

More information

CET Moving Charges & Magnetism

CET Moving Charges & Magnetism CET 2014 Moving Charges & Magnetism 1. When a charged particle moves perpendicular to the direction of uniform magnetic field its a) energy changes. b) momentum changes. c) both energy and momentum

More information

Chapter 5. Magnetostatics and Electromagnetic Induction

Chapter 5. Magnetostatics and Electromagnetic Induction Chapter 5. Magnetostatics and Electromagnetic Induction 5.1 Magnetic Field of Steady Currents The Lorentz force law The magnetic force in a charge q, moving with velocity v in a magnetic field B in a magnetic

More information

Induction and Inductance

Induction and Inductance Induction and Inductance How we generate E by B, and the passive component inductor in a circuit. 1. A review of emf and the magnetic flux. 2. Faraday s Law of Induction 3. Lentz Law 4. Inductance and

More information